LMFDB - Embedded newform 920.2.bo.a.373.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(37,920)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 22, 11, 42]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("920.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bo (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$2800$
Relative dimension:	$140$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			373.23
Character	$\chi$	$=$	920.373
Dual form			920.2.bo.a.37.23

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25883 - 0.644466i) q^{2} +(-0.0386486 - 0.540379i) q^{3} +(1.16933 + 1.62255i) q^{4} +(-1.40667 - 1.73819i) q^{5} +(-0.299603 + 0.705155i) q^{6} +(-0.537572 + 1.44129i) q^{7} +(-0.426313 - 2.79611i) q^{8} +(2.67895 - 0.385175i) q^{9} +O(q^{10})$	\(q+(-1.25883 - 0.644466i) q^{2} +(-0.0386486 - 0.540379i) q^{3} +(1.16933 + 1.62255i) q^{4} +(-1.40667 - 1.73819i) q^{5} +(-0.299603 + 0.705155i) q^{6} +(-0.537572 + 1.44129i) q^{7} +(-0.426313 - 2.79611i) q^{8} +(2.67895 - 0.385175i) q^{9} +(0.650559 + 3.09464i) q^{10} +(-5.97005 + 1.75297i) q^{11} +(0.831599 - 0.694590i) q^{12} +(1.18544 + 3.17828i) q^{13} +(1.60557 - 1.46789i) q^{14} +(-0.884913 + 0.827311i) q^{15} +(-1.26534 + 3.79459i) q^{16} +(5.61969 + 1.22249i) q^{17} +(-3.62058 - 1.24162i) q^{18} +(3.04272 - 4.73456i) q^{19} +(1.17544 - 4.31490i) q^{20} +(0.799616 + 0.234788i) q^{21} +(8.64504 + 1.64080i) q^{22} +(4.79583 + 0.00749698i) q^{23} +(-1.49448 + 0.338436i) q^{24} +(-1.04258 + 4.89009i) q^{25} +(0.556022 - 4.76489i) q^{26} +(-0.657155 - 3.02090i) q^{27} +(-2.96716 + 0.813098i) q^{28} +(-4.30083 + 2.76398i) q^{29} +(1.64713 - 0.471152i) q^{30} +(-3.75490 - 4.33338i) q^{31} +(4.03834 - 3.96129i) q^{32} +(1.17800 + 3.15834i) q^{33} +(-6.28640 - 5.16060i) q^{34} +(3.26140 - 1.09301i) q^{35} +(3.75754 + 3.89634i) q^{36} +(9.02827 + 6.75848i) q^{37} +(-6.88154 + 3.99910i) q^{38} +(1.67166 - 0.763420i) q^{39} +(-4.26049 + 4.67421i) q^{40} +(1.02414 - 7.12304i) q^{41} +(-0.855271 - 0.810885i) q^{42} +(4.00151 - 0.286194i) q^{43} +(-9.82523 - 7.63692i) q^{44} +(-4.43789 - 4.11470i) q^{45} +(-6.03232 - 3.10018i) q^{46} +(-2.13753 + 2.13753i) q^{47} +(2.09942 + 0.537108i) q^{48} +(3.50193 + 3.03444i) q^{49} +(4.46393 - 5.48391i) q^{50} +(0.443413 - 3.08401i) q^{51} +(-3.77075 + 5.63988i) q^{52} +(2.54878 - 6.83353i) q^{53} +(-1.11961 + 4.22632i) q^{54} +(11.4449 + 7.91122i) q^{55} +(4.25917 + 0.888673i) q^{56} +(-2.67605 - 1.46124i) q^{57} +(7.19533 - 0.707652i) q^{58} +(2.29366 - 5.02241i) q^{59} +(-2.37711 - 0.468418i) q^{60} +(4.58863 + 5.29556i) q^{61} +(1.93408 + 7.87491i) q^{62} +(-0.884980 + 4.06819i) q^{63} +(-7.63651 + 2.38404i) q^{64} +(3.85692 - 6.53128i) q^{65} +(0.552534 - 4.73501i) q^{66} +(5.95686 - 3.25269i) q^{67} +(4.58771 + 10.5477i) q^{68} +(-0.181301 - 2.59185i) q^{69} +(-4.80997 - 0.725947i) q^{70} +(1.40012 + 0.411113i) q^{71} +(-2.21906 - 7.32644i) q^{72} +(-0.620328 - 2.85160i) q^{73} +(-7.00949 - 14.3262i) q^{74} +(2.68280 + 0.374392i) q^{75} +(11.2400 - 0.599293i) q^{76} +(0.682807 - 9.54689i) q^{77} +(-2.59634 - 0.116306i) q^{78} +(-2.82351 + 6.18262i) q^{79} +(8.37562 - 3.13832i) q^{80} +(6.18357 - 1.81566i) q^{81} +(-5.87978 + 8.30671i) q^{82} +(7.12610 - 9.51935i) q^{83} +(0.554058 + 1.57196i) q^{84} +(-5.78011 - 11.4877i) q^{85} +(-5.22168 - 2.21856i) q^{86} +(1.65982 + 2.21725i) q^{87} +(7.44660 + 15.9456i) q^{88} +(4.42601 - 5.10789i) q^{89} +(2.93479 + 8.03979i) q^{90} -5.21806 q^{91} +(5.59573 + 7.79024i) q^{92} +(-2.19655 + 2.19655i) q^{93} +(4.06836 - 1.31323i) q^{94} +(-12.5096 + 1.37114i) q^{95} +(-2.29667 - 2.02913i) q^{96} +(-11.4468 + 8.56897i) q^{97} +(-2.45276 - 6.07673i) q^{98} +(-15.3183 + 6.99562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8}+O(q^{10}) $ 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8	$ 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8} - 22 q^{10} - 6 q^{12} - 44 q^{15} - 44 q^{16} - 44 q^{17} - 38 q^{18} - 22 q^{20} - 40 q^{23} - 36 q^{25} - 36 q^{26} - 22 q^{28} - 22 q^{30} - 104 q^{31} - 38 q^{32} - 44 q^{33} - 36 q^{36} - 22 q^{38} - 22 q^{40} - 72 q^{41} + 198 q^{42} - 28 q^{46} - 80 q^{47} - 10 q^{48} - 2 q^{50} - 146 q^{52} + 4 q^{55} - 44 q^{56} - 44 q^{57} - 42 q^{58} - 22 q^{60} + 46 q^{62} - 44 q^{63} - 44 q^{65} - 44 q^{66} - 64 q^{70} - 72 q^{71} - 104 q^{72} - 36 q^{73} - 44 q^{76} - 114 q^{78} - 220 q^{80} + 176 q^{81} - 10 q^{82} - 44 q^{86} - 12 q^{87} - 22 q^{88} - 440 q^{90} - 2 q^{92} - 76 q^{95} - 124 q^{96} - 44 q^{97} + 30 q^{98}+O(q^{100}) $ 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8 - 22 * q^10 - 6 * q^12 - 44 * q^15 - 44 * q^16 - 44 * q^17 - 38 * q^18 - 22 * q^20 - 40 * q^23 - 36 * q^25 - 36 * q^26 - 22 * q^28 - 22 * q^30 - 104 * q^31 - 38 * q^32 - 44 * q^33 - 36 * q^36 - 22 * q^38 - 22 * q^40 - 72 * q^41 + 198 * q^42 - 28 * q^46 - 80 * q^47 - 10 * q^48 - 2 * q^50 - 146 * q^52 + 4 * q^55 - 44 * q^56 - 44 * q^57 - 42 * q^58 - 22 * q^60 + 46 * q^62 - 44 * q^63 - 44 * q^65 - 44 * q^66 - 64 * q^70 - 72 * q^71 - 104 * q^72 - 36 * q^73 - 44 * q^76 - 114 * q^78 - 220 * q^80 + 176 * q^81 - 10 * q^82 - 44 * q^86 - 12 * q^87 - 22 * q^88 - 440 * q^90 - 2 * q^92 - 76 * q^95 - 124 * q^96 - 44 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{1}{22}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.25883	−	0.644466i	−0.890130	−	0.455706i
$2$	−1.25883	−	0.644466i	−0.890130	−	0.455706i
$3$	−0.0386486	−	0.540379i	−0.0223138	−	0.311988i	−0.996335	−	0.0855325i	$-0.972741\pi$
$3$	−0.0386486	−	0.540379i	−0.0223138	−	0.311988i	0.974022	−	0.226455i	$-0.0727137\pi$
$4$	1.16933	+	1.62255i	0.584664	+	0.811275i
$5$	−1.40667	−	1.73819i	−0.629080	−	0.777340i
$5$	−1.40667	−	1.73819i	−0.629080	−	0.777340i
$6$	−0.299603	+	0.705155i	−0.122312	+	0.287878i
$7$	−0.537572	+	1.44129i	−0.203183	+	0.544755i	−0.998076	−	0.0619944i	$-0.980254\pi$
$7$	−0.537572	+	1.44129i	−0.203183	+	0.544755i	0.794894	+	0.606749i	$0.207527\pi$
$8$	−0.426313	−	2.79611i	−0.150724	−	0.988576i
$9$	2.67895	−	0.385175i	0.892983	−	0.128392i
$10$	0.650559	+	3.09464i	0.205725	+	0.978610i
$11$	−5.97005	+	1.75297i	−1.80004	+	0.528539i	−0.997666	−	0.0682836i	$-0.978248\pi$
$11$	−5.97005	+	1.75297i	−1.80004	+	0.528539i	−0.802373	+	0.596823i	$0.796430\pi$
$12$	0.831599	−	0.694590i	0.240062	−	0.200511i
$13$	1.18544	+	3.17828i	0.328781	+	0.881495i	0.991201	+	0.132363i	$0.0422564\pi$
$13$	1.18544	+	3.17828i	0.328781	+	0.881495i	−0.662421	+	0.749132i	$0.730471\pi$
$14$	1.60557	−	1.46789i	0.429107	−	0.392311i
$15$	−0.884913	+	0.827311i	−0.228484	+	0.213611i
$16$	−1.26534	+	3.79459i	−0.316336	+	0.948647i
$17$	5.61969	+	1.22249i	1.36297	+	0.296497i	0.833824	−	0.552031i	$-0.186147\pi$
$17$	5.61969	+	1.22249i	1.36297	+	0.296497i	0.529151	+	0.848528i	$0.322511\pi$
$18$	−3.62058	−	1.24162i	−0.853380	−	0.292652i
$19$	3.04272	−	4.73456i	0.698048	−	1.08618i	−0.293439	−	0.955978i	$-0.594800\pi$
$19$	3.04272	−	4.73456i	0.698048	−	1.08618i	0.991487	−	0.130206i	$-0.0415638\pi$
$20$	1.17544	−	4.31490i	0.262836	−	0.964840i
$21$	0.799616	+	0.234788i	0.174491	+	0.0512351i
$22$	8.64504	+	1.64080i	1.84313	+	0.349820i
$23$	4.79583	+	0.00749698i	0.999999	+	0.00156323i
$23$	4.79583	+	0.00749698i	0.999999	+	0.00156323i
$24$	−1.49448	+	0.338436i	−0.305060	+	0.0690830i
$25$	−1.04258	+	4.89009i	−0.208516	+	0.978019i
$26$	0.556022	−	4.76489i	0.109045	−	0.934473i
$27$	−0.657155	−	3.02090i	−0.126470	−	0.581372i
$28$	−2.96716	+	0.813098i	−0.560740	+	0.153661i
$29$	−4.30083	+	2.76398i	−0.798645	+	0.513258i	−0.875173	−	0.483810i	$-0.839253\pi$
$29$	−4.30083	+	2.76398i	−0.798645	+	0.513258i	0.0765286	+	0.997067i	$0.475616\pi$
$30$	1.64713	−	0.471152i	0.300724	−	0.0860202i
$31$	−3.75490	−	4.33338i	−0.674400	−	0.778299i	0.310658	−	0.950522i	$-0.399450\pi$
$31$	−3.75490	−	4.33338i	−0.674400	−	0.778299i	−0.985058	+	0.172223i	$0.944905\pi$
$32$	4.03834	−	3.96129i	0.713884	−	0.700264i
$33$	1.17800	+	3.15834i	0.205063	+	0.549797i
$34$	−6.28640	−	5.16060i	−1.07811	−	0.885036i
$35$	3.26140	−	1.09301i	0.551278	−	0.184752i
$36$	3.75754	+	3.89634i	0.626256	+	0.649389i
$37$	9.02827	+	6.75848i	1.48424	+	1.11109i	0.966853	+	0.255334i	$0.0821855\pi$
$37$	9.02827	+	6.75848i	1.48424	+	1.11109i	0.517385	+	0.855753i	$0.326905\pi$
$38$	−6.88154	+	3.99910i	−1.11633	+	0.648740i
$39$	1.67166	−	0.763420i	0.267679	−	0.122245i
$40$	−4.26049	+	4.67421i	−0.673642	+	0.739058i
$41$	1.02414	−	7.12304i	0.159944	−	1.11243i	−0.738790	−	0.673936i	$-0.764602\pi$
$41$	1.02414	−	7.12304i	0.159944	−	1.11243i	0.898733	−	0.438496i	$-0.144489\pi$
$42$	−0.855271	−	0.810885i	−0.131971	−	0.125122i
$43$	4.00151	−	0.286194i	0.610224	−	0.0436441i	0.237193	−	0.971463i	$-0.423773\pi$
$43$	4.00151	−	0.286194i	0.610224	−	0.0436441i	0.373032	+	0.927819i	$0.378318\pi$
$44$	−9.82523	−	7.63692i	−1.48121	−	1.15131i
$45$	−4.43789	−	4.11470i	−0.661562	−	0.613383i
$46$	−6.03232	−	3.10018i	−0.889417	−	0.457097i
$47$	−2.13753	+	2.13753i	−0.311791	+	0.311791i	−0.845603	−	0.533812i	$-0.820759\pi$
$47$	−2.13753	+	2.13753i	−0.311791	+	0.311791i	0.533812	+	0.845603i	$0.320759\pi$
$48$	2.09942	+	0.537108i	0.303025	+	0.0775249i
$49$	3.50193	+	3.03444i	0.500275	+	0.433491i
$50$	4.46393	−	5.48391i	0.631295	−	0.775542i
$51$	0.443413	−	3.08401i	0.0620903	−	0.431847i
$52$	−3.77075	+	5.63988i	−0.522909	+	0.782110i
$53$	2.54878	−	6.83353i	0.350101	−	0.938658i	−0.635878	−	0.771790i	$-0.719362\pi$
$53$	2.54878	−	6.83353i	0.350101	−	0.938658i	0.985979	−	0.166868i	$-0.0533654\pi$
$54$	−1.11961	+	4.22632i	−0.152360	+	0.575129i
$55$	11.4449	+	7.91122i	1.54322	+	1.06675i
$56$	4.25917	+	0.888673i	0.569156	+	0.118754i
$57$	−2.67605	−	1.46124i	−0.354452	−	0.193546i
$58$	7.19533	−	0.707652i	0.944793	−	0.0929192i
$59$	2.29366	−	5.02241i	0.298609	−	0.653862i	−0.699546	−	0.714588i	$-0.746614\pi$
$59$	2.29366	−	5.02241i	0.298609	−	0.653862i	0.998154	+	0.0607259i	$0.0193416\pi$
$60$	−2.37711	−	0.468418i	−0.306883	−	0.0604725i
$61$	4.58863	+	5.29556i	0.587514	+	0.678027i	0.969203	−	0.246264i	$-0.0792030\pi$
$61$	4.58863	+	5.29556i	0.587514	+	0.678027i	−0.381689	+	0.924291i	$0.624658\pi$
$62$	1.93408	+	7.87491i	0.245628	+	1.00012i
$63$	−0.884980	+	4.06819i	−0.111497	+	0.512543i
$64$	−7.63651	+	2.38404i	−0.954564	+	0.298005i
$65$	3.85692	−	6.53128i	0.478392	−	0.810106i
$66$	0.552534	−	4.73501i	0.0680123	−	0.582839i
$67$	5.95686	−	3.25269i	0.727746	−	0.397379i	−0.0722484	−	0.997387i	$-0.523017\pi$
$67$	5.95686	−	3.25269i	0.727746	−	0.397379i	0.799995	+	0.600007i	$0.204836\pi$
$68$	4.58771	+	10.5477i	0.556341	+	1.27910i
$69$	−0.181301	−	2.59185i	−0.0218261	−	0.312022i
$70$	−4.80997	−	0.725947i	−0.574902	−	0.0867673i
$71$	1.40012	+	0.411113i	0.166164	+	0.0487901i	0.363756	−	0.931494i	$-0.381494\pi$
$71$	1.40012	+	0.411113i	0.166164	+	0.0487901i	−0.197592	+	0.980284i	$0.563312\pi$
$72$	−2.21906	−	7.32644i	−0.261519	−	0.863430i
$73$	−0.620328	−	2.85160i	−0.0726038	−	0.333754i	0.926490	−	0.376320i	$-0.122811\pi$
$73$	−0.620328	−	2.85160i	−0.0726038	−	0.333754i	−0.999094	+	0.0425653i	$0.986447\pi$
$74$	−7.00949	−	14.3262i	−0.814837	−	1.66539i
$75$	2.68280	+	0.374392i	0.309783	+	0.0432311i
$76$	11.2400	−	0.599293i	1.28932	−	0.0687436i
$77$	0.682807	−	9.54689i	0.0778131	−	1.08797i
$78$	−2.59634	−	0.116306i	−0.293977	−	0.0131690i
$79$	−2.82351	+	6.18262i	−0.317670	+	0.695599i	−0.999350	−	0.0360507i	$-0.988522\pi$
$79$	−2.82351	+	6.18262i	−0.317670	+	0.695599i	0.681680	+	0.731650i	$0.261249\pi$
$80$	8.37562	−	3.13832i	0.936422	−	0.350875i
$81$	6.18357	−	1.81566i	0.687063	−	0.201740i
$82$	−5.87978	+	8.30671i	−0.649313	+	0.917322i
$83$	7.12610	−	9.51935i	0.782191	−	1.04488i	−0.215469	−	0.976511i	$-0.569128\pi$
$83$	7.12610	−	9.51935i	0.782191	−	1.04488i	0.997660	−	0.0683737i	$-0.0217810\pi$
$84$	0.554058	+	1.57196i	0.0604526	+	0.171515i
$85$	−5.78011	−	11.4877i	−0.626941	−	1.24601i
$86$	−5.22168	−	2.21856i	−0.563068	−	0.239234i
$87$	1.65982	+	2.21725i	0.177951	+	0.237715i
$88$	7.44660	+	15.9456i	0.793811	+	1.69981i
$89$	4.42601	−	5.10789i	0.469156	−	0.541435i	−0.471020	−	0.882122i	$-0.656114\pi$
$89$	4.42601	−	5.10789i	0.469156	−	0.541435i	0.940177	+	0.340687i	$0.110660\pi$
$90$	2.93479	+	8.03979i	0.309354	+	0.847469i
$91$	−5.21806			−0.547001
$92$	5.59573	+	7.79024i	0.583395	+	0.812188i
$93$	−2.19655	+	2.19655i	−0.227771	+	0.227771i
$94$	4.06836	−	1.31323i	0.419619	−	0.135450i
$95$	−12.5096	+	1.37114i	−1.28346	+	0.140676i
$96$	−2.29667	−	2.02913i	−0.234403	−	0.207098i
$97$	−11.4468	+	8.56897i	−1.16225	+	0.870047i	−0.993298	−	0.115578i	$-0.963128\pi$
$97$	−11.4468	+	8.56897i	−1.16225	+	0.870047i	−0.168949	+	0.985625i	$0.554037\pi$
$98$	−2.45276	−	6.07673i	−0.247766	−	0.613842i
$99$	−15.3183	+	6.99562i	−1.53954	+	0.703086i
$100$	−9.15355	+	4.02649i	−0.915355	+	0.402649i
$101$	−5.27434	+	0.758335i	−0.524816	+	0.0754572i	−0.399631	−	0.916676i	$-0.630862\pi$
$101$	−5.27434	+	0.758335i	−0.524816	+	0.0754572i	−0.125185	+	0.992133i	$0.539953\pi$
$102$	−2.54572	+	3.59649i	−0.252064	+	0.356105i
$103$	5.66242	−	10.3699i	0.557935	−	1.02178i	−0.434693	−	0.900579i	$-0.643143\pi$
$103$	5.66242	−	10.3699i	0.557935	−	1.02178i	0.992628	−	0.121203i	$-0.0386751\pi$
$104$	8.38146	−	4.66955i	0.821869	−	0.457887i
$105$	−0.716687	−	1.72015i	−0.0699415	−	0.167870i
$106$	−7.61246	+	6.95969i	−0.739388	+	0.675985i
$107$	11.8030	+	0.844171i	1.14104	+	0.0816090i	0.629039	−	0.777374i	$-0.283449\pi$
$107$	11.8030	+	0.844171i	1.14104	+	0.0816090i	0.512005	+	0.858983i	$0.328903\pi$
$108$	4.13313	−	4.59869i	0.397710	−	0.442509i
$109$	−1.62182	−	2.52360i	−0.155342	−	0.241717i	0.754855	−	0.655891i	$-0.227707\pi$
$109$	−1.62182	−	2.52360i	−0.155342	−	0.241717i	−0.910198	+	0.414174i	$0.864071\pi$
$110$	−9.30867	−	17.3347i	−0.887546	−	1.65280i
$111$	3.30321	−	5.13989i	0.313527	−	0.487857i
$112$	−4.78887	−	3.86358i	−0.452506	−	0.365074i
$113$	4.99575	−	2.72789i	0.469961	−	0.256618i	−0.226773	−	0.973948i	$-0.572818\pi$
$113$	4.99575	−	2.72789i	0.469961	−	0.256618i	0.696734	+	0.717330i	$0.254636\pi$
$114$	2.42699	+	3.56408i	0.227309	+	0.333807i
$115$	−6.73310	−	8.34658i	−0.627864	−	0.778323i
$116$	−9.51378	−	3.74632i	−0.883332	−	0.347837i
$117$	4.39991	+	8.05784i	0.406772	+	0.744947i
$118$	−6.12410	+	4.84420i	−0.563769	+	0.445945i
$119$	−4.78294	+	7.44239i	−0.438451	+	0.682243i
$120$	2.69051	+	2.12162i	0.245609	+	0.193677i
$121$	23.3149	−	14.9836i	2.11953	−	1.36214i
$122$	−2.36352	−	9.62345i	−0.213983	−	0.871266i
$123$	−3.88872	−	0.278127i	−0.350634	−	0.0250779i
$124$	2.64043	−	11.1597i	0.237117	−	1.00217i
$125$	9.96645	−	5.06653i	0.891427	−	0.453165i
$126$	3.73585	−	4.55084i	0.332816	−	0.405421i
$127$	0.684550	−	1.25366i	0.0607440	−	0.111244i	−0.845543	−	0.533908i	$-0.820723\pi$
$127$	0.684550	−	1.25366i	0.0607440	−	0.111244i	0.906287	+	0.422663i	$0.138905\pi$
$128$	11.1495	+	1.92036i	0.985489	+	0.169738i
$129$	−0.309306	−	2.15127i	−0.0272329	−	0.189409i
$130$	−9.06441	+	5.73615i	−0.795001	+	0.503093i
$131$	−0.473214	+	0.216109i	−0.0413449	+	0.0188816i	−0.435980	−	0.899956i	$-0.643598\pi$
$131$	−0.473214	+	0.216109i	−0.0413449	+	0.0188816i	0.394635	+	0.918838i	$0.370871\pi$
$132$	−3.74710	+	5.60450i	−0.326143	+	0.487809i
$133$	5.18818	+	6.93059i	0.449872	+	0.600959i
$134$	−9.59495	+	0.255609i	−0.828877	+	0.0220813i
$135$	−4.32648	+	5.39165i	−0.372364	+	0.464039i
$136$	1.02247	−	16.2344i	0.0876763	−	1.39209i
$137$	7.69674	+	7.69674i	0.657577	+	0.657577i	0.954806	−	0.297229i	$-0.0960625\pi$
$137$	7.69674	+	7.69674i	0.657577	+	0.657577i	−0.297229	+	0.954806i	$0.596062\pi$
$138$	−1.44213	+	3.37955i	−0.122762	+	0.287687i
$139$	3.92888			0.333243			0.166621	−	0.986021i	$-0.446714\pi$
$139$	3.92888			0.333243			0.166621	+	0.986021i	$0.446714\pi$
$140$	5.58711	+	4.01371i	0.472197	+	0.339220i
$141$	1.23769	+	1.07246i	0.104232	+	0.0903177i
$142$	−1.49757	−	1.41985i	−0.125674	−	0.119151i
$143$	−12.6485	−	16.8964i	−1.05772	−	1.41295i
$144$	−1.92821	+	10.6529i	−0.160684	+	0.887741i
$145$	10.8541	+	3.58765i	0.901388	+	0.297938i
$146$	−1.05687	+	3.98947i	−0.0874670	+	0.330171i
$147$	1.50440	−	2.00964i	0.124081	−	0.165753i
$148$	−0.408962	+	22.5517i	−0.0336165	+	1.85374i
$149$	4.55588	+	15.5159i	0.373233	+	1.27111i	0.905431	+	0.424494i	$0.139548\pi$
$149$	4.55588	+	15.5159i	0.373233	+	1.27111i	−0.532198	+	0.846620i	$0.678634\pi$
$150$	−3.13592	−	2.20027i	−0.256046	−	0.179651i
$151$	1.26353	−	2.76674i	0.102825	−	0.225154i	−0.851226	−	0.524799i	$-0.824141\pi$
$151$	1.26353	−	2.76674i	0.102825	−	0.225154i	0.954051	+	0.299644i	$0.0968679\pi$
$152$	−14.5355	−	6.48939i	−1.17899	−	0.526359i
$153$	15.5257	+	1.11042i	1.25518	+	0.0897723i
$154$	−7.01219	+	11.5779i	−0.565058	+	0.932975i
$155$	−2.25034	+	12.6223i	−0.180751	+	1.01385i
$156$	3.19340	+	1.81966i	0.255677	+	0.145689i
$157$	9.34300	−	2.03245i	0.745653	−	0.162207i	0.176342	−	0.984329i	$-0.443574\pi$
$157$	9.34300	−	2.03245i	0.745653	−	0.162207i	0.569311	+	0.822122i	$0.307210\pi$
$158$	7.53882	−	5.96324i	0.599756	−	0.474410i
$159$	−3.79120	−	1.11320i	−0.300662	−	0.0882823i
$160$	−12.5661	−	1.44717i	−0.993434	−	0.114409i
$161$	−2.58890	+	6.90812i	−0.204034	+	0.544436i
$162$	−8.95421	−	1.69948i	−0.703510	−	0.133524i
$163$	−12.4100	+	6.77636i	−0.972024	+	0.530765i	−0.885076	−	0.465447i	$-0.845893\pi$
$163$	−12.4100	+	6.77636i	−0.972024	+	0.530765i	−0.0869487	+	0.996213i	$0.527712\pi$
$164$	12.7551	−	6.66746i	0.996002	−	0.520641i
$165$	3.83273	−	6.49031i	0.298378	−	0.505270i
$166$	−15.1055	+	7.39076i	−1.17241	+	0.573634i
$167$	−2.50344	+	11.5082i	−0.193722	+	0.890527i	0.772941	+	0.634478i	$0.218785\pi$
$167$	−2.50344	+	11.5082i	−0.193722	+	0.890527i	−0.966664	+	0.256050i	$0.917579\pi$
$168$	0.315609	−	2.33591i	0.0243498	−	0.180220i
$169$	1.12857	−	0.977910i	0.0868130	−	0.0752239i
$170$	−0.127216	+	18.1862i	−0.00975705	+	1.39482i
$171$	6.32766	−	13.8556i	0.483888	−	1.05957i
$172$	5.14344	+	6.15800i	0.392184	+	0.469543i
$173$	−4.61526	+	8.45222i	−0.350892	+	0.642611i	−0.992198	−	0.124675i	$-0.960211\pi$
$173$	−4.61526	+	8.45222i	−0.350892	+	0.642611i	0.641306	+	0.767286i	$0.278393\pi$
$174$	−0.660490	−	3.86085i	−0.0500716	−	0.292690i
$175$	−6.48756	−	4.13143i	−0.490413	−	0.312307i
$176$	0.902376	−	24.8720i	0.0680192	−	1.87480i
$177$	−2.80265	−	1.04533i	−0.210660	−	0.0785721i
$178$	−8.86348	+	3.57758i	−0.664346	+	0.268151i
$179$	−3.77223	+	26.2364i	−0.281950	+	1.96100i	−0.00546349	+	0.999985i	$0.501739\pi$
$179$	−3.77223	+	26.2364i	−0.281950	+	1.96100i	−0.276486	+	0.961018i	$0.589170\pi$
$180$	1.48695	−	12.0121i	0.110831	−	0.895332i
$181$	9.81364	−	11.3255i	0.729442	−	0.841821i	−0.262967	−	0.964805i	$-0.584701\pi$
$181$	9.81364	−	11.3255i	0.729442	−	0.841821i	0.992409	+	0.122984i	$0.0392464\pi$
$182$	6.56867	+	3.36286i	0.486902	+	0.249272i
$183$	2.68426	−	2.68426i	0.198426	−	0.198426i
$184$	−2.02356	−	13.4129i	−0.149179	−	0.988810i
$185$	−0.952273	−	25.1997i	−0.0700125	−	1.85272i
$186$	4.18069	−	1.34949i	0.306543	−	0.0989494i
$187$	−35.6928	+	2.55280i	−2.61012	+	0.186679i
$188$	−5.96772	−	0.968776i	−0.435241	−	0.0706553i
$189$	4.70724	+	0.676799i	0.342401	+	0.0492299i
$190$	16.6312	+	6.33600i	1.20656	+	0.459661i
$191$	−9.72098	+	4.43942i	−0.703385	+	0.321225i	−0.734803	−	0.678281i	$-0.762725\pi$
$191$	−9.72098	+	4.43942i	−0.703385	+	0.321225i	0.0314172	+	0.999506i	$0.489998\pi$
$192$	1.58342	+	4.03447i	0.114274	+	0.291163i
$193$	−4.85099	+	6.48016i	−0.349182	+	0.466452i	−0.940405	−	0.340055i	$-0.889554\pi$
$193$	−4.85099	+	6.48016i	−0.349182	+	0.466452i	0.591224	+	0.806508i	$0.298645\pi$
$194$	19.9320	−	3.40984i	1.43104	−	0.244813i
$195$	−3.67843	−	1.83177i	−0.263418	−	0.131176i
$196$	−0.828626	+	9.23031i	−0.0591876	+	0.659308i
$197$	−17.3722	+	6.47951i	−1.23772	+	0.461646i	−0.881245	−	0.472659i	$-0.843294\pi$
$197$	−17.3722	+	6.47951i	−1.23772	+	0.461646i	−0.356475	+	0.934305i	$0.616021\pi$
$198$	23.7916	+	1.06577i	1.69080	+	0.0757410i
$199$	−2.25724	−	2.60499i	−0.160011	−	0.184663i	0.670083	−	0.742287i	$-0.266259\pi$
$199$	−2.25724	−	2.60499i	−0.160011	−	0.184663i	−0.830094	+	0.557624i	$0.811713\pi$
$200$	14.1177	+	0.830462i	0.998274	+	0.0587225i
$201$	−1.98791	−	3.09325i	−0.140216	−	0.218181i
$202$	7.12824	+	2.44451i	0.501541	+	0.171995i
$203$	−1.67167	−	7.68456i	−0.117329	−	0.539351i
$204$	5.52245	−	2.88676i	0.386649	−	0.202113i
$205$	−13.8218	+	8.23960i	−0.965356	+	0.575479i
$206$	−13.8111	+	9.40481i	−0.962266	+	0.655264i
$207$	12.8507	−	1.82715i	0.893183	−	0.126995i
$208$	−13.5602	+	0.476634i	−0.940233	+	0.0330486i
$209$	−9.86567	+	33.5994i	−0.682423	+	2.32412i
$210$	−0.206387	+	2.62726i	−0.0142421	+	0.181299i
$211$	−1.70129	+	2.64725i	−0.117121	+	0.182244i	−0.894865	−	0.446338i	$-0.852728\pi$
$211$	−1.70129	+	2.64725i	−0.117121	+	0.182244i	0.777743	+	0.628582i	$0.216364\pi$
$212$	14.0681	−	3.85512i	0.966202	−	0.264771i
$213$	0.168044	−	0.772485i	0.0115142	−	0.0529298i
$214$	−14.3140	−	8.66933i	−0.978488	−	0.592623i
$215$	−6.12624	−	6.55279i	−0.417806	−	0.446896i
$216$	−8.16662	+	3.12533i	−0.555668	+	0.212652i
$217$	8.26417	−	3.08237i	0.561008	−	0.209245i
$218$	0.415229	+	4.22201i	0.0281229	+	0.285950i
$219$	−1.51697	+	0.445422i	−0.102507	+	0.0300988i
$220$	0.546429	+	27.8207i	0.0368402	+	1.87567i
$221$	2.77637	+	19.3101i	0.186759	+	1.29894i
$222$	−7.47067	+	4.34147i	−0.501399	+	0.291380i
$223$	−6.38761	+	17.1258i	−0.427746	+	1.14683i	0.527119	+	0.849791i	$0.323272\pi$
$223$	−6.38761	+	17.1258i	−0.427746	+	1.14683i	−0.954865	+	0.297040i	$0.904001\pi$
$224$	3.53845	+	7.94987i	0.236423	+	0.531173i
$225$	−0.909476	+	13.5019i	−0.0606318	+	0.900126i
$226$	−8.04685	+	0.214368i	−0.535269	+	0.0142596i
$227$	−0.500242	−	6.99429i	−0.0332022	−	0.464227i	−0.986670	−	0.162733i	$-0.947969\pi$
$227$	−0.500242	−	6.99429i	−0.0332022	−	0.464227i	0.953468	−	0.301494i	$-0.0974855\pi$
$228$	−0.758256	−	6.05070i	−0.0502168	−	0.400717i
$229$			17.1573i			1.13379i	0.823792	+	0.566893i	$0.191855\pi$
$229$			17.1573i			1.13379i	−0.823792	+	0.566893i	$0.808145\pi$
$230$	3.09677	+	14.8462i	0.204195	+	0.978930i
$231$	−5.18533			−0.341170
$232$	9.56190	+	10.8473i	0.627769	+	0.712160i
$233$	0.0676152	−	0.00483593i	0.00442962	−	0.000316812i	−0.0691242	−	0.997608i	$-0.522020\pi$
$233$	0.0676152	−	0.00483593i	0.00442962	−	0.000316812i	0.0735538	+	0.997291i	$0.476566\pi$
$234$	−0.345762	−	12.9791i	−0.0226032	−	0.848469i
$235$	6.72221	+	0.708633i	0.438509	+	0.0462261i
$236$	10.8312	−	2.15127i	0.705048	−	0.140036i
$237$	3.45008	+	1.28681i	0.224107	+	0.0835876i
$238$	10.8173	−	6.28630i	0.701181	−	0.407481i
$239$	−14.1770	+	2.03835i	−0.917034	+	0.131850i	−0.584642	−	0.811291i	$-0.698765\pi$
$239$	−14.1770	+	2.03835i	−0.917034	+	0.131850i	−0.332393	+	0.943141i	$0.607856\pi$
$240$	−2.01959	−	4.40471i	−0.130364	−	0.284323i
$241$	−3.21297	−	10.9424i	−0.206966	−	0.704860i	−0.995906	−	0.0903910i	$-0.971188\pi$
$241$	−3.21297	−	10.9424i	−0.206966	−	0.704860i	0.788941	−	0.614469i	$-0.210630\pi$
$242$	−39.0059	+	3.83619i	−2.50740	+	0.246599i
$243$	−4.46128	−	11.9612i	−0.286192	−	0.767309i
$244$	−3.22670	+	13.6375i	−0.206568	+	0.873053i
$245$	0.348372	−	10.3554i	0.0222567	−	0.661585i
$246$	4.71601	+	2.85626i	0.300682	+	0.182109i
$247$	18.6547	+	4.05808i	1.18697	+	0.258209i
$248$	−10.5159	+	12.3465i	−0.667759	+	0.784004i
$249$	−5.41947	−	3.48288i	−0.343445	−	0.220719i
$250$	−15.8113	−	0.0451079i	−0.999996	−	0.00285287i
$251$	13.3026	+	3.90599i	0.839651	+	0.246544i	0.673158	−	0.739499i	$-0.264937\pi$
$251$	13.3026	+	3.90599i	0.839651	+	0.246544i	0.166493	+	0.986043i	$0.446756\pi$
$252$	−7.63567	+	3.32112i	−0.481002	+	0.209211i
$253$	−28.6445	+	8.36216i	−1.80086	+	0.525725i
$254$	−1.66967	+	1.13698i	−0.104765	+	0.0713405i
$255$	−5.98431	+	3.56743i	−0.374752	+	0.223401i
$256$	−12.7978	−	9.60291i	−0.799864	−	0.600182i
$257$	−7.22168	+	1.57098i	−0.450476	+	0.0979950i	−0.432079	−	0.901836i	$-0.642220\pi$
$257$	−7.22168	+	1.57098i	−0.450476	+	0.0979950i	−0.0183969	+	0.999831i	$0.505856\pi$
$258$	−0.997054	+	2.90743i	−0.0620739	+	0.181009i
$259$	−14.5942	+	9.37914i	−0.906841	+	0.582792i
$260$	15.1073	−	1.37916i	0.936917	−	0.0855319i
$261$	−10.4571	+	9.06113i	−0.647278	+	0.560870i
$262$	0.734973	+	0.0329239i	0.0454068	+	0.00203404i
$263$	4.38774	+	11.7640i	0.270560	+	0.725399i	0.999180	+	0.0404815i	$0.0128892\pi$
$263$	4.38774	+	11.7640i	0.270560	+	0.725399i	−0.728620	+	0.684918i	$0.759838\pi$
$264$	8.32889	−	4.64026i	0.512607	−	0.285589i
$265$	−15.4632	+	5.18225i	−0.949898	+	0.318343i
$266$	−2.06453	−	12.0681i	−0.126584	−	0.739941i
$267$	−2.93126	−	2.19431i	−0.179390	−	0.134290i
$268$	12.2432	+	5.86184i	0.747871	+	0.358069i
$269$	−7.08320	−	15.5101i	−0.431871	−	0.945665i	−0.993020	−	0.117950i	$-0.962368\pi$
$269$	−7.08320	−	15.5101i	−0.431871	−	0.945665i	0.561149	−	0.827715i	$-0.310359\pi$
$270$	8.92105	−	3.99893i	0.542918	−	0.243367i
$271$	−1.09629	+	7.62486i	−0.0665948	+	0.463177i	0.929050	+	0.369953i	$0.120626\pi$
$271$	−1.09629	+	7.62486i	−0.0665948	+	0.463177i	−0.995645	+	0.0932239i	$0.970283\pi$
$272$	−11.7497	+	19.7775i	−0.712428	+	1.19919i
$273$	0.201671	+	2.81973i	0.0122057	+	0.170658i
$274$	−4.72864	−	14.6492i	−0.285668	−	0.884991i
$275$	−2.34791	−	31.0217i	−0.141585	−	1.87068i
$276$	3.99341	−	3.32490i	0.240375	−	0.200135i
$277$	5.93919	+	5.93919i	0.356851	+	0.356851i	0.862651	−	0.505800i	$-0.168803\pi$
$277$	5.93919	+	5.93919i	0.356851	+	0.356851i	−0.505800	+	0.862651i	$0.668803\pi$
$278$	−4.94581	−	2.53203i	−0.296630	−	0.151861i
$279$	−11.7283	−	10.1626i	−0.702154	−	0.608420i
$280$	−4.44655	−	8.65330i	−0.265732	−	0.517134i
$281$	24.8810	+	3.57735i	1.48428	+	0.213407i	0.836308	−	0.548260i	$-0.184710\pi$
$281$	24.8810	+	3.57735i	1.48428	+	0.213407i	0.647969	+	0.761667i	$0.275619\pi$
$282$	−0.866879	−	2.14770i	−0.0516219	−	0.127894i
$283$	−0.00621271	+	0.0166569i	−0.000369307	+	0.000990151i	−0.937134	−	0.348969i	$-0.886532\pi$
$283$	−0.00621271	+	0.0166569i	−0.000369307	+	0.000990151i	0.936765	+	0.349959i	$0.113805\pi$
$284$	0.970151	+	2.75250i	0.0575679	+	0.163331i
$285$	1.22442	+	6.70695i	0.0725281	+	0.397286i
$286$	5.03322	+	29.4214i	0.297620	+	1.73972i
$287$	9.71578	+	5.30522i	0.573505	+	0.313157i
$288$	9.29271	−	12.1676i	0.547578	−	0.716980i
$289$	14.6226	+	6.67794i	0.860156	+	0.392820i
$290$	−11.3515	−	11.5114i	−0.666580	−	0.675972i
$291$	5.07289	+	5.85443i	0.297378	+	0.343193i
$292$	3.90150	−	4.34097i	0.228318	−	0.254036i
$293$	0.463974	+	0.100931i	0.0271056	+	0.00589647i	0.226098	−	0.974105i	$-0.427403\pi$
$293$	0.463974	+	0.100931i	0.0271056	+	0.00589647i	−0.198992	+	0.980001i	$0.563767\pi$
$294$	−3.18894	+	1.56027i	−0.185983	+	0.0909971i
$295$	−11.9563	+	3.07805i	−0.696122	+	0.179211i
$296$	15.0486	−	28.1253i	0.874683	−	1.63475i
$297$	9.21878	+	16.8829i	0.534928	+	0.979647i
$298$	4.26437	−	22.4681i	0.247028	−	1.30154i
$299$	5.66131	+	15.2513i	0.327402	+	0.882008i
$300$	2.52960	+	4.79076i	0.146047	+	0.276595i
$301$	−1.73861	+	5.92116i	−0.100212	+	0.341290i
$302$	−3.37365	+	2.66857i	−0.194131	+	0.153559i
$303$	0.613634	+	2.82083i	0.0352524	+	0.162053i
$304$	14.1156	+	17.5367i	0.809588	+	1.00580i
$305$	2.75000	−	15.4250i	0.157464	−	0.883231i
$306$	−18.8287	−	11.4036i	−1.07636	−	0.651902i
$307$	−1.00867	+	14.1031i	−0.0575680	+	0.804906i	0.883873	+	0.467727i	$0.154927\pi$
$307$	−1.00867	+	14.1031i	−0.0575680	+	0.804906i	−0.941441	+	0.337178i	$0.890527\pi$
$308$	16.2887	−	10.0556i	0.928138	−	0.572969i
$309$	−5.82254	−	2.65907i	−0.331233	−	0.151269i
$310$	10.9675	−	14.4392i	0.622910	−	0.820089i
$311$	−17.8060	+	5.22831i	−1.00968	+	0.296470i	−0.744424	−	0.667707i	$-0.767276\pi$
$311$	−17.8060	+	5.22831i	−1.00968	+	0.296470i	−0.265260	+	0.964177i	$0.585458\pi$
$312$	−2.84726	−	4.34869i	−0.161194	−	0.246196i
$313$	−15.1047	−	11.3072i	−0.853766	−	0.639121i	0.0800830	−	0.996788i	$-0.474481\pi$
$313$	−15.1047	−	11.3072i	−0.853766	−	0.639121i	−0.933849	+	0.357667i	$0.883572\pi$
$314$	−13.0711	−	3.46273i	−0.737647	−	0.195413i
$315$	8.31614	−	4.18432i	0.468561	−	0.235760i
$316$	−13.3332	+	2.64823i	−0.750053	+	0.148975i
$317$	−1.62546	+	1.21680i	−0.0912949	+	0.0683425i	−0.643950	−	0.765067i	$-0.722706\pi$
$317$	−1.62546	+	1.21680i	−0.0912949	+	0.0683425i	0.552655	+	0.833410i	$0.313615\pi$
$318$	4.05508	+	3.84463i	0.227398	+	0.215596i
$319$	20.8310	−	24.0403i	1.16631	−	1.34600i
$320$	14.8859	+	9.92013i	0.832149	+	0.554552i
$321$		−	6.41074i		−	0.357813i
$322$	7.71105	−	7.02772i	0.429720	−	0.391640i
$323$	22.8871	−	22.8871i	1.27347	−	1.27347i
$324$	10.1766	+	7.91005i	0.565368	+	0.439447i
$325$	−16.7780	+	2.48329i	−0.930675	+	0.137748i
$326$	19.9892	−	0.532513i	1.10710	−	0.0294932i
$327$	−1.30102	+	0.973932i	−0.0719466	+	0.0538586i
$328$	−20.3534	+	0.173034i	−1.12383	+	0.00955420i
$329$	−1.93171	−	4.22986i	−0.106499	−	0.233200i
$330$	−9.00756	+	5.70017i	−0.495850	+	0.313784i
$331$	20.3914	−	2.93185i	1.12082	−	0.161149i	0.443099	−	0.896473i	$-0.353879\pi$
$331$	20.3914	−	2.93185i	1.12082	−	0.161149i	0.677716	+	0.735324i	$0.262970\pi$
$332$	23.7784	+	0.431207i	1.30501	+	0.0236656i
$333$	26.7895	+	14.6282i	1.46805	+	0.801618i
$334$	10.5680	−	12.8735i	0.578257	−	0.704405i
$335$	−14.0331	−	5.77868i	−0.766710	−	0.315723i
$336$	−1.90271	+	2.73713i	−0.103802	+	0.149323i
$337$	1.50893	−	21.0976i	0.0821968	−	1.14926i	−0.774199	−	0.632942i	$-0.781847\pi$
$337$	1.50893	−	21.0976i	0.0821968	−	1.14926i	0.856396	−	0.516319i	$-0.172698\pi$
$338$	−2.05091	+	0.503704i	−0.111555	+	0.0273979i
$339$	−1.66717	−	2.59417i	−0.0905483	−	0.140896i
$340$	11.8805	−	22.8114i	0.644311	−	1.23712i
$341$	30.0132	+	19.2883i	1.62531	+	1.04452i
$342$	−16.8950	+	13.3640i	−0.913574	+	0.722642i
$343$	−15.7068	+	8.57656i	−0.848087	+	0.463091i
$344$	−2.50612	−	11.0667i	−0.135121	−	0.596675i
$345$	−4.25009	+	3.96101i	−0.228817	+	0.213253i
$346$	11.2570	−	7.66557i	0.605181	−	0.412104i
$347$	7.44709	+	13.6383i	0.399781	+	0.732144i	0.997582	−	0.0695004i	$-0.0221405\pi$
$347$	7.44709	+	13.6383i	0.399781	+	0.732144i	−0.597801	+	0.801645i	$0.703959\pi$
$348$	−1.65674	+	5.28584i	−0.0888105	+	0.283351i
$349$	−8.79848	−	5.65444i	−0.470972	−	0.302675i	0.283542	−	0.958960i	$-0.408491\pi$
$349$	−8.79848	−	5.65444i	−0.470972	−	0.302675i	−0.754513	+	0.656285i	$0.772127\pi$
$350$	5.50420	+	9.38179i	0.294212	+	0.501478i
$351$	8.82222	−	5.66970i	0.470895	−	0.302626i
$352$	−17.1651	+	30.7282i	−0.914903	+	1.63782i
$353$	1.68159	−	23.5117i	0.0895020	−	1.25140i	−0.732043	−	0.681258i	$-0.761433\pi$
$353$	1.68159	−	23.5117i	0.0895020	−	1.25140i	0.821545	−	0.570143i	$-0.193112\pi$
$354$	2.85439	+	3.12211i	0.151709	+	0.165938i
$355$	−1.25491	−	3.01197i	−0.0666039	−	0.159859i
$356$	13.4633	+	1.20863i	0.713552	+	0.0640572i
$357$	4.20657	+	2.29696i	0.222635	+	0.121568i
$358$	21.6571	−	30.5963i	1.14461	−	1.61706i
$359$	0.0155942	+	0.108460i	0.000823033	+	0.00572432i	0.990229	−	0.139452i	$-0.0445341\pi$
$359$	0.0155942	+	0.108460i	0.000823033	+	0.00572432i	−0.989406	+	0.145176i	$0.953625\pi$
$360$	−9.61324	+	14.1630i	−0.506662	+	0.746456i
$361$	−5.26507	−	11.5289i	−0.277109	−	0.606784i
$362$	−19.6527	+	7.93243i	−1.03292	+	0.416919i
$363$	−8.99788	−	12.0198i	−0.472266	−	0.630874i
$364$	−6.10162	−	8.46656i	−0.319812	−	0.443768i
$365$	−4.08402	+	5.08949i	−0.213767	+	0.266396i
$366$	−5.10896	+	1.64913i	−0.267050	+	0.0862013i
$367$	5.62632	+	5.62632i	0.293691	+	0.293691i	0.838537	−	0.544845i	$-0.183412\pi$
$367$	5.62632	+	5.62632i	0.293691	+	0.293691i	−0.544845	+	0.838537i	$0.683412\pi$
$368$	−6.09681	+	18.1887i	−0.317818	+	0.948152i
$369$		−	19.4767i		−	1.01392i
$370$	−15.0416	+	32.3360i	−0.781976	+	1.68107i
$371$	8.47892	+	7.34702i	0.440203	+	0.381438i
$372$	−6.13249	−	0.995524i	−0.317955	−	0.0516155i
$373$	−3.81605	+	2.85666i	−0.197588	+	0.147912i	−0.693491	−	0.720466i	$-0.743928\pi$
$373$	−3.81605	+	2.85666i	−0.197588	+	0.147912i	0.495903	+	0.868378i	$0.334837\pi$
$374$	46.5765	+	19.7892i	2.40841	+	1.02328i
$375$	−3.12304	−	5.18985i	−0.161273	−	0.268002i
$376$	6.88803	+	5.06552i	0.355223	+	0.261234i
$377$	−13.8830	−	10.3927i	−0.715013	−	0.535252i
$378$	−5.48946	−	3.88563i	−0.282347	−	0.199855i
$379$	−3.71311	−	12.6457i	−0.190730	−	0.649565i	−0.998217	−	0.0596812i	$-0.980992\pi$
$379$	−3.71311	−	12.6457i	−0.190730	−	0.649565i	0.807488	−	0.589884i	$-0.200827\pi$
$380$	−16.8526	−	18.6942i	−0.864521	−	0.958993i
$381$	−0.703908	−	0.321464i	−0.0360623	−	0.0164691i
$382$	15.0982	+	0.676338i	0.772489	+	0.0346045i
$383$	28.9222	+	2.06855i	1.47785	+	0.105698i	0.786846	−	0.617149i	$-0.211713\pi$
$383$	28.9222	+	2.06855i	1.47785	+	0.105698i	0.691008	+	0.722848i	$0.257167\pi$
$384$	0.606807	−	6.09919i	0.0309660	−	0.311248i
$385$	−17.5548	+	12.2424i	−0.894673	+	0.623933i
$386$	10.2828	−	5.03116i	0.523382	−	0.256079i
$387$	10.6096	−	2.30798i	0.539316	−	0.117321i
$388$	−27.2887	−	8.55308i	−1.38537	−	0.434217i
$389$	4.93737	−	16.8151i	0.250335	−	0.852562i	−0.734432	−	0.678682i	$-0.762551\pi$
$389$	4.93737	−	16.8151i	0.250335	−	0.852562i	0.984767	−	0.173880i	$-0.0556304\pi$
$390$	3.45002	+	4.67652i	0.174699	+	0.236805i
$391$	26.9419	+	5.90497i	1.36251	+	0.298627i
$392$	6.99172	−	11.0854i	0.353135	−	0.559898i
$393$	0.135070	+	0.247362i	0.00681338	+	0.0124778i
$394$	26.0446	+	3.03918i	1.31211	+	0.153112i
$395$	14.7183	−	3.78910i	0.740557	−	0.190650i
$396$	−29.2628	−	16.6745i	−1.47051	−	0.837925i
$397$	33.4589	+	7.27853i	1.67925	+	0.365299i	0.948360	−	0.317195i	$-0.102741\pi$
$397$	33.4589	+	7.27853i	1.67925	+	0.365299i	0.730891	+	0.682494i	$0.239105\pi$
$398$	1.16266	+	4.73396i	0.0582789	+	0.237292i
$399$	3.54463	−	3.07144i	0.177453	−	0.153764i
$400$	−17.2367	−	10.1438i	−0.861834	−	0.507190i
$401$	−16.0200	−	7.31609i	−0.800001	−	0.365348i	−0.0269054	−	0.999638i	$-0.508565\pi$
$401$	−16.0200	−	7.31609i	−0.800001	−	0.365348i	−0.773095	+	0.634290i	$0.781293\pi$
$402$	0.508958	+	5.17503i	0.0253845	+	0.258107i
$403$	9.32149	−	17.0710i	0.464337	−	0.850369i
$404$	−7.39787	−	7.67114i	−0.368058	−	0.381653i
$405$	−11.8542	−	8.19416i	−0.589038	−	0.407171i
$406$	−2.84807	+	10.7509i	−0.141348	+	0.533560i
$407$	−65.7466	−	24.5222i	−3.25894	−	1.21552i
$408$	−8.81227	+	0.0749171i	−0.436272	+	0.00370895i
$409$	−28.6217	−	4.11517i	−1.41525	−	0.203482i	−0.608115	−	0.793849i	$-0.708074\pi$
$409$	−28.6217	−	4.11517i	−1.41525	−	0.203482i	−0.807135	+	0.590367i	$0.798983\pi$
$410$	22.7095	−	1.46462i	1.12154	−	0.0723326i
$411$	3.86169	−	4.45663i	0.190483	−	0.219829i
$412$	23.4470	−	2.93831i	1.15515	−	0.144760i
$413$	6.00572	+	6.00572i	0.295522	+	0.295522i
$414$	−17.3544	−	5.98173i	−0.852922	−	0.293986i
$415$	−26.5704	+	1.00407i	−1.30429	+	0.0492879i
$416$	17.3773	+	8.13910i	0.851990	+	0.399052i
$417$	−0.151846	−	2.12308i	−0.00743592	−	0.103968i
$418$	34.0729	−	35.9380i	1.66656	−	1.75778i
$419$	−30.3185	−	4.35914i	−1.48116	−	0.212958i	−0.646155	−	0.763206i	$-0.723624\pi$
$419$	−30.3185	−	4.35914i	−1.48116	−	0.212958i	−0.835001	+	0.550248i	$0.814533\pi$
$420$	1.95299	−	3.17428i	0.0952961	−	0.154889i
$421$	−16.3876	−	35.8839i	−0.798685	−	1.74888i	−0.649920	−	0.760003i	$-0.725198\pi$
$421$	−16.3876	−	35.8839i	−0.798685	−	1.74888i	−0.148764	−	0.988873i	$-0.547530\pi$
$422$	3.84770	−	2.23603i	0.187303	−	0.108848i
$423$	−4.90301	+	6.54966i	−0.238393	+	0.318455i
$424$	−20.1939	−	4.21345i	−0.980703	−	0.204623i
$425$	−11.8371	+	26.2063i	−0.574181	+	1.27119i
$426$	−0.709380	+	0.864133i	−0.0343696	+	0.0418674i
$427$	−10.0991	+	3.76678i	−0.488731	+	0.182287i
$428$	12.4319	+	20.1382i	0.600920	+	0.973414i
$429$	−8.64163	+	7.48802i	−0.417222	+	0.361525i
$430$	3.48888	+	12.1970i	0.168249	+	0.588193i
$431$	−12.3314	−	19.1880i	−0.593983	−	0.924255i	−0.999946	−	0.0103661i	$-0.996700\pi$
$431$	−12.3314	−	19.1880i	−0.593983	−	0.924255i	0.405963	−	0.913889i	$-0.366936\pi$
$432$	12.2946	+	1.32883i	0.591523	+	0.0639334i
$433$	−11.2320	+	2.44337i	−0.539775	+	0.117421i	−0.474184	−	0.880426i	$-0.657257\pi$
$433$	−11.2320	+	2.44337i	−0.539775	+	0.117421i	−0.0655911	+	0.997847i	$0.520893\pi$
$434$	−12.3897	−	1.44577i	−0.594725	−	0.0693992i
$435$	1.51919	−	6.00401i	0.0728397	−	0.287870i
$436$	2.19823	−	5.58241i	0.105276	−	0.267349i
$437$	14.6278	−	22.6833i	0.699745	−	1.08509i
$438$	2.19667	+	0.416921i	0.104961	+	0.0199213i
$439$	6.80275	−	23.1680i	0.324677	−	1.10575i	−0.621853	−	0.783134i	$-0.713620\pi$
$439$	6.80275	−	23.1680i	0.324677	−	1.10575i	0.946530	−	0.322616i	$-0.104562\pi$
$440$	17.2416	−	35.3738i	0.821961	−	1.68638i
$441$	10.5503	+	6.78025i	0.502394	+	0.322869i
$442$	8.94969	−	26.0975i	0.425694	−	1.24133i
$443$	−1.21497	+	5.58511i	−0.0577248	+	0.265356i	−0.996960	−	0.0779185i	$-0.975173\pi$
$443$	−1.21497	+	5.58511i	−0.0577248	+	0.265356i	0.939235	+	0.343275i	$0.111536\pi$
$444$	12.2023	−	0.650598i	0.579094	−	0.0308760i
$445$	−15.1044	−	0.508134i	−0.716017	−	0.0240879i
$446$	19.0780	−	17.4420i	0.903368	−	0.825903i
$447$	8.20839	−	3.06157i	0.388244	−	0.144807i
$448$	0.669094	−	12.2880i	0.0316117	−	0.580553i
$449$	0.155910	+	0.530982i	0.00735786	+	0.0250586i	0.963090	−	0.269179i	$-0.0867524\pi$
$449$	0.155910	+	0.530982i	0.00735786	+	0.0250586i	−0.955732	+	0.294238i	$0.904934\pi$
$450$	9.84638	−	16.4105i	0.464163	−	0.773599i
$451$	6.37229	+	44.3202i	0.300059	+	2.08696i
$452$	10.2678	+	4.91607i	0.482957	+	0.231232i
$453$	−1.54392	−	0.575854i	−0.0725398	−	0.0270560i
$454$	−3.87786	+	9.12704i	−0.181997	+	0.428353i
$455$	7.34006	+	9.06995i	0.344108	+	0.425206i
$456$	−2.94495	+	8.10550i	−0.137910	+	0.379575i
$457$	−20.8677	+	1.49249i	−0.976149	+	0.0698156i	−0.550290	−	0.834974i	$-0.685483\pi$
$457$	−20.8677	+	1.49249i	−0.976149	+	0.0698156i	−0.425860	+	0.904789i	$0.640028\pi$
$458$	11.0573	−	21.5982i	0.516673	−	1.00922i
$459$		−	17.7798i		−	0.829892i
$460$	5.66955	−	20.6847i	0.264344	−	0.964428i
$461$		−	15.7540i		−	0.733735i	−0.930273	−	0.366868i	$-0.880430\pi$
$461$		−	15.7540i		−	0.733735i	0.930273	−	0.366868i	$-0.119570\pi$
$462$	6.52747	+	3.34177i	0.303685	+	0.155473i
$463$	0.929043	−	0.0664465i	0.0431763	−	0.00308803i	−0.0497343	−	0.998762i	$-0.515837\pi$
$463$	0.929043	−	0.0664465i	0.0431763	−	0.00308803i	0.0929106	+	0.995674i	$0.470383\pi$
$464$	−5.04613	−	19.8173i	−0.234261	−	0.919994i
$465$	6.90781	+	0.728198i	0.320342	+	0.0337694i
$466$	−0.0882329	−	0.0374880i	−0.00408731	−	0.00173660i
$467$	−11.6310	−	4.33815i	−0.538220	−	0.200746i	0.0656292	−	0.997844i	$-0.479095\pi$
$467$	−11.6310	−	4.33815i	−0.538220	−	0.200746i	−0.603850	+	0.797098i	$0.706367\pi$
$468$	−7.92931	+	16.5613i	−0.366532	+	0.765548i
$469$	1.48582	+	10.3341i	0.0686087	+	0.477184i
$470$	−8.00547	−	5.22429i	−0.369265	−	0.240978i
$471$	−1.45938	−	4.97021i	−0.0672449	−	0.229015i
$472$	−15.0210	−	4.27221i	−0.691400	−	0.196644i
$473$	−23.3875	+	8.72310i	−1.07536	+	0.401089i
$474$	−3.51378	−	3.84335i	−0.161393	−	0.176531i
$475$	19.9802	+	19.8153i	0.916754	+	0.909191i
$476$	−17.6685	+	0.942045i	−0.809834	+	0.0431786i
$477$	4.19594	−	19.2884i	0.192119	−	0.883155i
$478$	19.1602	+	6.57065i	0.876365	+	0.300535i
$479$	30.6063	+	19.6695i	1.39844	+	0.898720i	0.999831	−	0.0184020i	$-0.00585786\pi$
$479$	30.6063	+	19.6695i	1.39844	+	0.898720i	0.398606	+	0.917122i	$0.369494\pi$
$480$	−0.296358	+	6.84636i	−0.0135268	+	0.312492i
$481$	−10.7779	+	36.7061i	−0.491429	+	1.67365i
$482$	−3.00738	+	15.8453i	−0.136983	+	0.721733i
$483$	3.83306	+	1.13200i	0.174410	+	0.0515078i
$484$	51.5743	+	20.3089i	2.34429	+	0.923130i
$485$	30.9963	+	7.84299i	1.40747	+	0.356132i
$486$	−2.09254	+	17.9323i	−0.0949196	+	0.813424i
$487$	24.1626	−	5.25625i	1.09491	−	0.238183i	0.371384	−	0.928479i	$-0.378883\pi$
$487$	24.1626	−	5.25625i	1.09491	−	0.238183i	0.723527	+	0.690296i	$0.242520\pi$
$488$	12.8508	−	15.0879i	0.581728	−	0.682997i
$489$	4.14143	+	6.44419i	0.187282	+	0.291416i
$490$	−7.11227	+	12.8113i	−0.321300	+	0.578754i
$491$	−29.0515	+	25.1732i	−1.31107	+	1.13605i	−0.329671	+	0.944096i	$0.606938\pi$
$491$	−29.0515	+	25.1732i	−1.31107	+	1.13605i	−0.981403	+	0.191957i	$0.938517\pi$
$492$	−4.09592	−	6.63487i	−0.184658	−	0.299123i
$493$	−27.5483	+	10.2750i	−1.24071	+	0.462761i
$494$	−20.8679	−	17.1308i	−0.938890	−	0.770749i
$495$	33.7074	+	16.7855i	1.51503	+	0.754452i
$496$	21.1946	−	8.76508i	0.951667	−	0.393564i
$497$	−1.34520	+	1.79697i	−0.0603403	+	0.0806053i
$498$	4.57762	+	7.87703i	0.205128	+	0.352978i
$499$	13.1173	+	28.7228i	0.587210	+	1.28581i	0.937114	+	0.349024i	$0.113487\pi$
$499$	13.1173	+	28.7228i	0.587210	+	1.28581i	−0.349904	+	0.936786i	$0.613786\pi$
$500$	19.8748	+	10.2466i	0.888827	+	0.458244i
$501$	6.31551	+	0.908034i	0.282156	+	0.0405680i
$502$	−14.2285	−	13.4900i	−0.635048	−	0.602090i
$503$	−0.867390	−	12.1277i	−0.0386750	−	0.540747i	−0.979446	−	0.201705i	$-0.935352\pi$
$503$	−0.867390	−	12.1277i	−0.0386750	−	0.540747i	0.940771	−	0.339042i	$-0.110103\pi$
$504$	11.7524	+	0.740186i	0.523493	+	0.0329705i
$505$	8.73736	+	8.10105i	0.388807	+	0.360492i
$506$	41.4478	+	7.93380i	1.84258	+	0.352701i
$507$	−0.572060	−	0.572060i	−0.0254061	−	0.0254061i
$508$	2.83459	−	0.355222i	0.125765	−	0.0157604i
$509$	20.5804	−	23.7511i	0.912212	−	1.05275i	−0.0861926	−	0.996278i	$-0.527470\pi$
$509$	20.5804	−	23.7511i	0.912212	−	1.05275i	0.998404	−	0.0564699i	$-0.0179845\pi$
$510$	9.83234	−	0.634126i	0.435383	−	0.0280796i
$511$	4.44344	+	0.638870i	0.196566	+	0.0282619i
$512$	9.92159	+	20.3362i	0.438476	+	0.898743i
$513$	−16.3022	−	6.08039i	−0.719758	−	0.268456i
$514$	10.1033	+	2.67652i	0.445639	+	0.118056i
$515$	−25.9900	+	4.74472i	−1.14526	+	0.209077i
$516$	3.12886	−	3.01740i	0.137741	−	0.132834i
$517$	9.01415	−	16.5082i	0.396442	−	0.726029i
$518$	24.4163	−	2.40131i	1.07279	−	0.105507i
$519$	4.74578	+	2.16732i	0.208316	+	0.0951349i
$520$	−19.9065	−	8.00002i	−0.872956	−	0.350824i
$521$	−9.01512	+	7.81164i	−0.394959	+	0.342234i	−0.829589	−	0.558375i	$-0.811425\pi$
$521$	−9.01512	+	7.81164i	−0.394959	+	0.342234i	0.434629	+	0.900610i	$0.356879\pi$
$522$	19.0033	−	4.66722i	0.831754	−	0.204279i
$523$	−9.41389	−	2.04787i	−0.411641	−	0.0895469i	0.00197606	−	0.999998i	$-0.499371\pi$
$523$	−9.41389	−	2.04787i	−0.411641	−	0.0895469i	−0.413617	+	0.910451i	$0.635735\pi$
$524$	−0.903991	−	0.515110i	−0.0394910	−	0.0225027i
$525$	−1.98180	+	3.66541i	−0.0864929	+	0.159972i
$526$	2.05805	−	17.6367i	0.0897351	−	0.768996i
$527$	−15.8038	−	28.9426i	−0.688426	−	1.26076i
$528$	−13.4752	+	0.473645i	−0.586432	+	0.0206127i
$529$	22.9999	+	0.0719084i	0.999995	+	0.00312645i
$530$	22.8054	+	3.44192i	0.990604	+	0.149507i
$531$	4.21009	−	14.3382i	0.182702	−	0.622226i
$532$	−5.17856	+	16.5222i	−0.224519	+	0.716329i
$533$	23.8530	−	5.18891i	1.03319	−	0.224757i
$534$	2.27581	+	4.65137i	0.0984838	+	0.201284i
$535$	−15.1356	−	21.7034i	−0.654370	−	0.938318i
$536$	−11.6344	−	15.2694i	−0.502529	−	0.659538i
$537$	14.3234	+	1.02443i	0.618100	+	0.0442074i
$538$	−1.07911	+	24.0895i	−0.0465239	+	1.03857i
$539$	−26.2260	−	11.9770i	−1.12963	−	0.515886i
$540$	−13.8073	−	0.715322i	−0.594172	−	0.0307826i
$541$	−1.02824	−	3.50188i	−0.0442077	−	0.150557i	0.934432	−	0.356143i	$-0.115908\pi$
$541$	−1.02824	−	3.50188i	−0.0442077	−	0.150557i	−0.978639	+	0.205585i	$0.934090\pi$
$542$	6.29401	−	8.89192i	0.270351	−	0.381940i
$543$	−6.49937	−	4.86536i	−0.278915	−	0.208793i
$544$	27.5368	−	17.3244i	1.18063	−	0.742777i
$545$	−2.10513	+	6.36890i	−0.0901739	+	0.272814i
$546$	1.56335	−	3.67954i	0.0669051	−	0.157470i
$547$	29.8246	−	22.3264i	1.27521	−	0.954610i	0.275232	−	0.961378i	$-0.411245\pi$
$547$	29.8246	−	22.3264i	1.27521	−	0.954610i	0.999977	+	0.00676807i	$0.00215436\pi$
$548$	−3.48834	+	21.4884i	−0.149014	+	0.917938i
$549$	14.3324	+	12.4191i	0.611693	+	0.530035i
$550$	−17.0368	+	40.5644i	−0.726452	+	1.72967i
$551$			28.7726i			1.22575i
$552$	−7.16982	+	1.61188i	−0.305168	+	0.0686061i
$553$	−7.39308	−	7.39308i	−0.314386	−	0.314386i
$554$	−3.64885	−	11.3041i	−0.155025	−	0.480263i
$555$	−13.5806	+	1.48852i	−0.576464	+	0.0631843i
$556$	4.59415	+	6.37480i	0.194835	+	0.270352i
$557$	−4.73904	−	6.33061i	−0.200799	−	0.268237i	0.688827	−	0.724926i	$-0.258126\pi$
$557$	−4.73904	−	6.33061i	−0.200799	−	0.268237i	−0.889626	+	0.456689i	$0.849035\pi$
$558$	8.21452	+	20.3515i	0.347748	+	0.861549i
$559$	5.65313	+	12.3786i	0.239102	+	0.523560i
$560$	0.0207227	+	13.7587i	0.000875692	+	0.581412i
$561$	2.75896	+	19.1890i	0.116483	+	0.810159i
$562$	−29.0156	−	20.5382i	−1.22395	−	0.866353i
$563$	−14.4739	−	7.90333i	−0.610001	−	0.333086i	0.144380	−	0.989522i	$-0.453881\pi$
$563$	−14.4739	−	7.90333i	−0.610001	−	0.333086i	−0.754381	+	0.656437i	$0.772063\pi$
$564$	−0.292862	+	3.26227i	−0.0123317	+	0.137366i
$565$	−11.7689	−	4.84632i	−0.495123	−	0.203886i
$566$	0.0185556	−	0.0169644i	0.000779949	−	0.000713068i
$567$	−0.707227	+	9.88833i	−0.0297007	+	0.415271i
$568$	0.552629	−	4.09017i	0.0231878	−	0.171620i
$569$	11.0416	−	7.09602i	0.462889	−	0.297481i	−0.288333	−	0.957530i	$-0.593101\pi$
$569$	11.0416	−	7.09602i	0.462889	−	0.297481i	0.751222	+	0.660049i	$0.229465\pi$
$570$	2.78106	−	9.23204i	0.116486	−	0.386687i
$571$	25.9933	+	16.7049i	1.08779	+	0.699078i	0.956343	−	0.292245i	$-0.0944024\pi$
$571$	25.9933	+	16.7049i	1.08779	+	0.699078i	0.131444	+	0.991324i	$0.458039\pi$
$572$	12.6251	−	40.2804i	0.527881	−	1.68421i
$573$	2.77467	+	5.08143i	0.115914	+	0.212280i
$574$	−8.81153	−	12.9399i	−0.367786	−	0.540100i
$575$	−5.03669	+	23.4442i	−0.210045	+	0.977692i
$576$	−19.5396	+	9.32811i	−0.814148	+	0.388671i
$577$	11.2091	−	6.12061i	0.466639	−	0.254804i	−0.228685	−	0.973500i	$-0.573443\pi$
$577$	11.2091	−	6.12061i	0.466639	−	0.254804i	0.695324	+	0.718696i	$0.255261\pi$
$578$	−14.1038	−	17.8302i	−0.586640	−	0.741639i
$579$	3.68923	+	2.37092i	0.153319	+	0.0985321i
$580$	6.87091	+	21.8065i	0.285299	+	0.905468i
$581$	9.88931	+	15.3881i	0.410278	+	0.638405i
$582$	−2.61295	−	10.6391i	−0.108310	−	0.441003i
$583$	−3.23738	+	45.2645i	−0.134079	+	1.87466i
$584$	−7.70895	+	2.95018i	−0.318998	+	0.122079i
$585$	7.81681	−	18.9826i	0.323185	−	0.784832i
$586$	−0.519019	−	0.426071i	−0.0214405	−	0.0176008i
$587$	−3.45894	−	1.88872i	−0.142766	−	0.0779560i	0.406278	−	0.913749i	$-0.366826\pi$
$587$	−3.45894	−	1.88872i	−0.142766	−	0.0779560i	−0.549044	+	0.835793i	$0.685008\pi$
$588$	5.01989	+	0.0910328i	0.207017	+	0.00375413i
$589$	−31.9418	+	4.59253i	−1.31614	+	0.189232i
$590$	17.0347	+	3.83066i	0.701307	+	0.157706i
$591$	4.17280	+	9.13716i	0.171646	+	0.375853i
$592$	−37.0695	+	25.7068i	−1.52355	+	1.05654i
$593$	25.8835	−	19.3761i	1.06291	−	0.795681i	0.0832828	−	0.996526i	$-0.473460\pi$
$593$	25.8835	−	19.3761i	1.06291	−	0.795681i	0.979623	+	0.200845i	$0.0643686\pi$
$594$	−0.724448	−	27.1940i	−0.0297245	−	1.11578i
$595$	19.6643	−	2.15533i	0.806156	−	0.0883601i
$596$	−19.8480	+	25.5354i	−0.813007	+	1.04597i
$597$	−1.32044	+	1.32044i	−0.0540421	+	0.0540421i
$598$	2.70231	−	22.8474i	0.110506	−	0.934301i
$599$			20.5361i			0.839083i	0.907736	+	0.419541i	$0.137809\pi$
$599$			20.5361i			0.839083i	−0.907736	+	0.419541i	$0.862191\pi$
$600$	−0.0968671	−	7.66102i	−0.00395458	−	0.312760i
$601$	4.38344	−	5.05876i	0.178804	−	0.206351i	−0.659271	−	0.751905i	$-0.729135\pi$
$601$	4.38344	−	5.05876i	0.178804	−	0.206351i	0.838076	+	0.545554i	$0.183681\pi$
$602$	6.00461	−	6.33329i	0.244730	−	0.258126i
$603$	14.7053	−	11.0082i	0.598845	−	0.448290i
$604$	5.96666	−	1.18509i	0.242780	−	0.0482207i
$605$	−58.8404	−	19.4487i	−2.39220	−	0.790702i
$606$	1.04546	−	3.94643i	0.0424691	−	0.160313i
$607$	−19.5786	−	14.6564i	−0.794673	−	0.594885i	0.122915	−	0.992417i	$-0.460776\pi$
$607$	−19.5786	−	14.6564i	−0.794673	−	0.594885i	−0.917588	+	0.397533i	$0.869867\pi$
$608$	−6.46745	−	31.1729i	−0.262290	−	1.26423i
$609$	−4.08797	+	1.20034i	−0.165653	+	0.0486400i
$610$	−13.4027	+	17.6452i	−0.542658	+	0.714434i
$611$	−9.32756	−	4.25975i	−0.377353	−	0.172331i
$612$	16.3530	+	26.4897i	0.661029	+	1.07078i
$613$	1.21196	−	16.9454i	0.0489506	−	0.684419i	−0.912436	−	0.409219i	$-0.865801\pi$
$613$	1.21196	−	16.9454i	0.0489506	−	0.684419i	0.961387	−	0.275200i	$-0.0887441\pi$
$614$	10.3587	−	17.1034i	0.418043	−	0.690237i
$615$	4.98670	+	7.15055i	0.201083	+	0.288338i
$616$	−26.9853	+	2.16075i	−1.08727	+	0.0870593i
$617$	9.67682	+	44.4836i	0.389574	+	1.79084i	0.585985	+	0.810322i	$0.300708\pi$
$617$	9.67682	+	44.4836i	0.389574	+	1.79084i	−0.196411	+	0.980522i	$0.562929\pi$
$618$	5.61594	+	7.09975i	0.225906	+	0.285594i
$619$	1.33133	−	4.53408i	0.0535105	−	0.182240i	−0.928401	−	0.371579i	$-0.878816\pi$
$619$	1.33133	−	4.53408i	0.0535105	−	0.182240i	0.981912	+	0.189339i	$0.0606346\pi$
$620$	−23.1118	+	11.1084i	−0.928191	+	0.446123i
$621$	−3.12896	−	14.4926i	−0.125561	−	0.581569i
$622$	25.7842	+	4.89377i	1.03385	+	0.196222i
$623$	4.98263	+	9.12500i	0.199625	+	0.365586i
$624$	0.781648	+	7.30924i	0.0312909	+	0.292604i
$625$	−22.8261	−	10.1966i	−0.913042	−	0.407865i
$626$	11.7272	+	23.9683i	0.468712	+	0.957968i
$627$	18.5377	+	4.03263i	0.740324	+	0.161048i
$628$	14.2228	+	12.7829i	0.567551	+	0.510093i
$629$	42.4739	+	49.0175i	1.69354	+	1.95445i
$630$	−13.1653	−	0.0920941i	−0.524518	−	0.00366912i
$631$	−8.93533	−	4.08063i	−0.355710	−	0.162447i	0.229542	−	0.973299i	$-0.426277\pi$
$631$	−8.93533	−	4.08063i	−0.355710	−	0.162447i	−0.585252	+	0.810851i	$0.699004\pi$
$632$	18.4910	+	5.25912i	0.735533	+	0.209197i
$633$	1.49627	+	0.817026i	0.0594715	+	0.0324739i
$634$	2.83037	−	0.484202i	0.112409	−	0.0192301i
$635$	−3.14203	+	0.573606i	−0.124687	+	0.0227628i
$636$	−2.62694	−	7.45311i	−0.104165	−	0.295535i
$637$	−5.49297	+	14.7272i	−0.217639	+	0.583514i
$638$	−41.7160	+	16.8379i	−1.65155	+	0.666618i
$639$	3.90921	+	0.562059i	0.154646	+	0.0222347i
$640$	−12.3457	−	22.0813i	−0.488008	−	0.872839i
$641$	−6.04133	−	5.23484i	−0.238618	−	0.206764i	0.527340	−	0.849654i	$-0.323189\pi$
$641$	−6.04133	−	5.23484i	−0.238618	−	0.206764i	−0.765958	+	0.642891i	$0.777735\pi$
$642$	−4.13150	+	8.07006i	−0.163057	+	0.318500i
$643$	9.07923	+	9.07923i	0.358050	+	0.358050i	0.863094	−	0.505044i	$-0.168524\pi$
$643$	9.07923	+	9.07923i	0.358050	+	0.358050i	−0.505044	+	0.863094i	$0.668524\pi$
$644$	−14.2361	+	3.87723i	−0.560979	+	0.152784i
$645$	−3.30422	+	3.56375i	−0.130103	+	0.140322i
$646$	−43.5610	+	14.0611i	−1.71388	+	0.553227i
$647$	−1.81902	−	25.4333i	−0.0715131	−	0.999884i	−0.898872	−	0.438211i	$-0.855612\pi$
$647$	−1.81902	−	25.4333i	−0.0715131	−	0.999884i	0.827359	−	0.561673i	$-0.189842\pi$
$648$	−7.71292	−	16.5159i	−0.302992	−	0.648807i
$649$	−4.88915	+	34.0048i	−0.191916	+	1.33480i
$650$	22.7211	+	7.68678i	0.891194	+	0.301500i
$651$	−1.98505	−	4.34665i	−0.0778002	−	0.170359i
$652$	−25.5063	−	12.2120i	−0.998905	−	0.478260i
$653$	−25.3589	−	18.9834i	−0.992370	−	0.742879i	−0.0259014	−	0.999665i	$-0.508246\pi$
$653$	−25.3589	−	18.9834i	−0.992370	−	0.742879i	−0.966468	+	0.256786i	$0.917336\pi$
$654$	2.26544	−	0.387556i	0.0885855	−	0.0151546i
$655$	1.04129	+	0.518539i	0.0406866	+	0.0202610i
$656$	25.7331	+	12.8993i	1.00471	+	0.503632i
$657$	−2.76019	−	7.40036i	−0.107685	−	0.288715i
$658$	−0.294293	+	6.56962i	−0.0114727	+	0.256111i
$659$	−28.9719	+	25.1043i	−1.12858	+	0.977923i	−0.999905	−	0.0137630i	$-0.995619\pi$
$659$	−28.9719	+	25.1043i	−1.12858	+	0.977923i	−0.128678	+	0.991686i	$0.541074\pi$
$660$	15.0126	−	1.37051i	0.584364	−	0.0533470i
$661$	−2.20301	+	1.41579i	−0.0856873	+	0.0550679i	−0.582783	−	0.812628i	$-0.698036\pi$
$661$	−2.20301	+	1.41579i	−0.0856873	+	0.0550679i	0.497096	+	0.867696i	$0.334400\pi$
$662$	−27.5589	−	9.45087i	−1.07111	−	0.367319i
$663$	10.3275	−	2.24660i	0.401085	−	0.0872508i
$664$	−29.6551	−	15.8672i	−1.15084	−	0.615765i
$665$	4.74862	−	18.7670i	0.184144	−	0.727755i
$666$	−24.2962	−	35.6793i	−0.941457	−	1.38255i
$667$	−20.6468	+	13.2233i	−0.799446	+	0.512009i
$668$	−21.5999	+	9.39484i	−0.835726	+	0.363497i
$669$	9.50132	+	2.78984i	0.367342	+	0.107861i
$670$	13.9412	+	16.3182i	0.538595	+	0.630429i
$671$	−36.6773	−	23.5711i	−1.41591	−	0.909951i
$672$	4.15919	−	2.21936i	0.160444	−	0.0856135i
$673$	−19.3635	−	4.21228i	−0.746410	−	0.162372i	−0.176754	−	0.984255i	$-0.556560\pi$
$673$	−19.3635	−	4.21228i	−0.746410	−	0.162372i	−0.569656	+	0.821883i	$0.692923\pi$
$674$	−15.4962	+	25.5860i	−0.596891	+	0.985534i
$675$	15.4576	−	0.0640293i	0.594963	−	0.00246449i
$676$	2.90638	+	0.687662i	0.111784	+	0.0264485i
$677$	7.93291	+	21.2689i	0.304886	+	0.817432i	0.995548	+	0.0942541i	$0.0300466\pi$
$677$	7.93291	+	21.2689i	0.304886	+	0.817432i	−0.690662	+	0.723178i	$0.742681\pi$
$678$	0.426840	+	4.34006i	0.0163927	+	0.166679i
$679$	−6.19685	−	21.1045i	−0.237813	−	0.809918i
$680$	−29.6568	+	21.0592i	−1.13729	+	0.807584i
$681$	−3.76023	+	0.540640i	−0.144092	+	0.0207174i
$682$	−25.3510	−	43.6233i	−0.970740	−	1.67042i
$683$	32.9355	+	12.2843i	1.26024	+	0.470046i	0.888751	−	0.458391i	$-0.151574\pi$
$683$	32.9355	+	12.2843i	1.26024	+	0.470046i	0.371491	+	0.928437i	$0.378847\pi$
$684$	29.8806	−	5.93484i	1.14251	−	0.226924i
$685$	2.55162	−	24.2051i	0.0974924	−	0.924830i
$686$	25.2996	−	0.673980i	0.965942	−	0.0257327i
$687$	9.27144	−	0.663106i	0.353727	−	0.0252991i
$688$	−3.97729	+	15.5462i	−0.151633	+	0.592694i
$689$	24.7403			0.942529
$690$	7.90289	−	2.24721i	0.300858	−	0.0855500i
$691$		−	4.41290i		−	0.167875i	−0.996471	−	0.0839374i	$-0.973250\pi$
$691$		−	4.41290i		−	0.167875i	0.996471	−	0.0839374i	$-0.0267496\pi$
$692$	−19.1109	+	2.39493i	−0.726488	+	0.0910414i
$693$	−1.84802	−	25.8386i	−0.0702003	−	0.981529i
$694$	−0.585222	−	21.9678i	−0.0222147	−	0.833886i
$695$	−5.52662	−	6.82912i	−0.209637	−	0.259043i
$696$	5.49210	−	5.58628i	0.208177	−	0.211747i
$697$	14.4632	−	38.7773i	0.547832	−	1.46879i
$698$	7.43174	+	12.7883i	0.281295	+	0.484045i
$699$	−0.00522647	−	0.0363509i	−0.000197683	−	0.00137492i
$700$	−0.882632	−	15.3574i	−0.0333604	−	0.580455i
$701$	−48.6318	+	14.2796i	−1.83680	+	0.539332i	−0.999967	−	0.00813003i	$-0.997412\pi$
$701$	−48.6318	+	14.2796i	−1.83680	+	0.539332i	−0.836830	+	0.547462i	$0.815594\pi$
$702$	−14.7596	+	1.45159i	−0.557067	+	0.0547868i
$703$	59.4689	−	22.1808i	2.24291	−	0.836563i
$704$	41.4113	−	27.6194i	1.56075	−	1.04094i
$705$	0.123125	−	3.65993i	0.00463717	−	0.137841i
$706$	−17.2693	+	28.5136i	−0.649940	+	1.07312i
$707$	1.74236	−	8.00948i	0.0655281	−	0.301228i
$708$	−1.58111	−	5.76978i	−0.0594217	−	0.216842i
$709$	22.8739	−	35.5925i	0.859049	−	1.33671i	−0.0813688	−	0.996684i	$-0.525929\pi$
$709$	22.8739	−	35.5925i	0.859049	−	1.33671i	0.940418	−	0.340022i	$-0.110434\pi$
$710$	−0.361383	+	4.60032i	−0.0135625	+	0.172647i
$711$	−5.18265	+	17.6505i	−0.194364	+	0.661944i
$712$	−16.1691	−	10.1981i	−0.605963	−	0.382189i
$713$	−17.9753	−	20.8103i	−0.673182	−	0.779352i
$714$	−3.81506	−	5.60248i	−0.142775	−	0.209667i
$715$	−11.5769	+	45.7531i	−0.432952	+	1.71107i
$716$	−46.9809	+	24.5584i	−1.75576	+	0.917789i
$717$	1.64940	+	7.58217i	0.0615980	+	0.283162i
$718$	0.0502684	−	0.146584i	0.00187600	−	0.00547045i
$719$	−21.6166	−	33.6360i	−0.806162	−	1.25441i	−0.963723	−	0.266903i	$-0.914000\pi$
$719$	−21.6166	−	33.6360i	−0.806162	−	1.25441i	0.157561	−	0.987509i	$-0.449637\pi$
$720$	21.2290	−	11.6335i	0.791160	−	0.433554i
$721$	11.9021	+	13.7357i	0.443257	+	0.511546i
$722$	−0.802124	+	17.9061i	−0.0298520	+	0.666397i
$723$	−5.78885	+	2.15913i	−0.215290	+	0.0802989i
$724$	29.8516	+	2.67985i	1.10943	+	0.0995958i
$725$	−9.03215	−	23.9132i	−0.335446	−	0.888112i
$726$	3.58052	+	20.9297i	0.132886	+	0.776775i
$727$	28.0144	−	37.4229i	1.03900	−	1.38794i	0.120407	−	0.992725i	$-0.461580\pi$
$727$	28.0144	−	37.4229i	1.03900	−	1.38794i	0.918590	−	0.395212i	$-0.129329\pi$
$728$	2.22452	+	14.5903i	0.0824463	+	0.540752i
$729$	11.2956	−	5.15851i	0.418354	−	0.191056i
$730$	8.42110	−	3.77482i	0.311679	−	0.139712i
$731$	22.8371	+	3.28348i	0.844660	+	0.121444i
$732$	7.49414	+	1.21657i	0.276991	+	0.0449657i
$733$	−0.199333	+	0.0142566i	−0.00736255	+	0.000526580i	−0.0750200	−	0.997182i	$-0.523902\pi$
$733$	−0.199333	+	0.0142566i	−0.00736255	+	0.000526580i	0.0676574	+	0.997709i	$0.478448\pi$
$734$	−3.45663	−	10.7086i	−0.127587	−	0.395260i
$735$	−5.60932	+	0.211971i	−0.206903	+	0.00781866i
$736$	19.3969	−	18.9674i	0.714978	−	0.699147i
$737$	−29.8609	+	29.8609i	−1.09994	+	1.09994i
$738$	−12.5521	+	24.5180i	−0.462049	+	0.902519i
$739$	−17.9799	+	20.7499i	−0.661401	+	0.763298i	−0.983005	−	0.183576i	$-0.941233\pi$
$739$	−17.9799	+	20.7499i	−0.661401	+	0.763298i	0.321604	+	0.946874i	$0.395778\pi$
$740$	39.7743	−	31.0119i	1.46213	−	1.14002i
$741$	1.47192	−	10.2374i	0.0540724	−	0.376082i
$742$	−5.93865	−	14.7131i	−0.218015	−	0.540133i
$743$	−2.17980	−	0.813024i	−0.0799691	−	0.0298270i	0.309161	−	0.951010i	$-0.399952\pi$
$743$	−2.17980	−	0.813024i	−0.0799691	−	0.0298270i	−0.389130	+	0.921183i	$0.627224\pi$
$744$	7.07821	+	5.20538i	0.259500	+	0.190838i
$745$	20.5609	−	29.7447i	0.753295	−	1.08976i
$746$	6.64480	−	1.13675i	0.243283	−	0.0416194i
$747$	15.4238	−	28.2466i	0.564329	−	1.03349i
$748$	−45.8787	−	54.9283i	−1.67749	−	2.00838i
$749$	−7.56167	+	16.5578i	−0.276297	+	0.605007i
$750$	0.586711	+	8.54585i	0.0214237	+	0.312050i
$751$	11.1759	−	9.68399i	0.407815	−	0.353374i	−0.426667	−	0.904409i	$-0.640312\pi$
$751$	11.1759	−	9.68399i	0.407815	−	0.353374i	0.834482	+	0.551035i	$0.185767\pi$
$752$	−5.40634	−	10.8158i	−0.197149	−	0.394410i
$753$	1.59659	−	7.33939i	0.0581829	−	0.267462i
$754$	10.7787	+	22.0298i	0.392537	+	0.802280i
$755$	−6.58648	+	1.69564i	−0.239706	+	0.0617105i
$756$	4.40617	+	8.42913i	0.160251	+	0.306565i
$757$	31.4396	−	17.1673i	1.14269	−	0.623958i	0.207549	−	0.978225i	$-0.433451\pi$
$757$	31.4396	−	17.1673i	1.14269	−	0.623958i	0.935144	+	0.354267i	$0.115270\pi$
$758$	−3.47552	+	18.3118i	−0.126237	+	0.665115i
$759$	5.62581	+	15.1557i	0.204204	+	0.550116i
$760$	9.16689	+	34.3939i	0.332518	+	1.24760i
$761$	−3.83237	−	1.12529i	−0.138923	−	0.0407916i	0.211532	−	0.977371i	$-0.432155\pi$
$761$	−3.83237	−	1.12529i	−0.138923	−	0.0407916i	−0.350455	+	0.936580i	$0.613973\pi$
$762$	0.678931	+	0.858314i	0.0245951	+	0.0310934i
$763$	4.50908	−	0.980890i	0.163240	−	0.0355106i
$764$	−18.5702	−	10.5816i	−0.671846	−	0.382830i
$765$	−19.9094	−	28.5486i	−0.719826	−	1.03218i
$766$	−35.0751	−	21.2433i	−1.26732	−	0.767552i
$767$	18.6816	+	1.33613i	0.674553	+	0.0482450i
$768$	−4.69459	+	7.28681i	−0.169401	+	0.262940i
$769$	−17.3613	+	38.0159i	−0.626064	+	1.37089i	0.284962	+	0.958539i	$0.408019\pi$
$769$	−17.3613	+	38.0159i	−0.626064	+	1.37089i	−0.911026	+	0.412349i	$0.864708\pi$
$770$	29.9884	−	4.09778i	1.08071	−	0.147674i
$771$	1.12803	+	3.84173i	0.0406251	+	0.138356i
$772$	−16.1868	−	0.293538i	−0.582575	−	0.0105647i
$773$	−7.48488	+	9.99863i	−0.269213	+	0.359626i	−0.914692	−	0.404152i	$-0.867567\pi$
$773$	−7.48488	+	9.99863i	−0.269213	+	0.359626i	0.645479	+	0.763778i	$0.276658\pi$
$774$	−14.8431	−	3.93216i	−0.533526	−	0.141339i
$775$	25.1054	−	13.8439i	0.901814	−	0.497288i
$776$	28.8397	+	28.3535i	1.03529	+	1.01783i
$777$	5.63234	+	7.52392i	0.202059	+	0.269919i
$778$	−17.0521	+	17.9855i	−0.611348	+	0.644812i
$779$	−30.6083	−	26.5223i	−1.09666	−	0.950259i
$780$	−1.32915	−	8.11038i	−0.0475911	−	0.290398i
$781$	−9.07947			−0.324889
$782$	−30.1098	−	24.7965i	−1.07672	−	0.886720i
$783$	11.1760	+	11.1760i	0.399398	+	0.399398i
$784$	−15.9456	+	9.44877i	−0.569485	+	0.337456i
$785$	−16.6753	−	13.3809i	−0.595165	−	0.477585i
$786$	−0.0106143	−	0.398436i	−0.000378601	−	0.0142117i
$787$	23.3988	+	31.2571i	0.834077	+	1.11420i	0.991937	+	0.126734i	$0.0404496\pi$
$787$	23.3988	+	31.2571i	0.834077	+	1.11420i	−0.157860	+	0.987461i	$0.550460\pi$
$788$	−30.8272	−	20.6107i	−1.09817	−	0.734224i
$789$	6.18743	−	2.82571i	0.220279	−	0.100598i
$790$	−20.9698	−	4.71557i	−0.746073	−	0.167772i
$791$	1.24609	+	8.66674i	0.0443058	+	0.308154i
$792$	26.0909	+	39.8493i	0.927101	+	1.41598i
$793$	−11.3912	+	20.8615i	−0.404514	+	0.740812i
$794$	−37.4284	−	30.7255i	−1.32828	−	1.09041i
$795$	3.39801	+	8.15571i	0.120515	+	0.289253i
$796$	1.58728	−	6.70857i	0.0562595	−	0.237779i
$797$	−5.16471	−	0.369387i	−0.182943	−	0.0130844i	−0.0204331	−	0.999791i	$-0.506505\pi$
$797$	−5.16471	−	0.369387i	−0.182943	−	0.0130844i	−0.162510	+	0.986707i	$0.551959\pi$
$798$	−6.44154	+	1.58204i	−0.228028	+	0.0560037i
$799$	−14.6253	+	9.39914i	−0.517408	+	0.332518i
$800$	15.1608	+	23.8778i	0.536015	+	0.844208i
$801$	9.88963	−	15.3886i	0.349433	−	0.543728i
$802$	15.4516	+	19.5341i	0.545614	+	0.689772i
$803$	8.70215	+	15.9368i	0.307092	+	0.562397i
$804$	2.69443	−	6.84251i	0.0950253	−	0.241317i
$805$	15.6493	−	5.21743i	0.551566	−	0.183890i
$806$	−22.7359	+	15.4822i	−0.800839	+	0.545338i
$807$	−8.10755	+	4.42705i	−0.285399	+	0.155840i
$808$	4.36891	+	14.4244i	0.153698	+	0.507447i
$809$	−7.06957	+	11.0005i	−0.248553	+	0.386756i	−0.943003	−	0.332785i	$-0.892012\pi$
$809$	−7.06957	+	11.0005i	−0.248553	+	0.386756i	0.694450	+	0.719541i	$0.255648\pi$
$810$	9.64158	+	17.9547i	0.338771	+	0.630864i
$811$	−10.1382	−	15.7754i	−0.356001	−	0.553948i	0.616350	−	0.787472i	$-0.288611\pi$
$811$	−10.1382	−	15.7754i	−0.356001	−	0.553948i	−0.972351	+	0.233524i	$0.924974\pi$
$812$	10.5139	−	11.6982i	0.368964	−	0.410525i
$813$	4.16268	+	0.297721i	0.145992	+	0.0104415i
$814$	66.9604	+	73.2409i	2.34696	+	2.56709i
$815$	29.2353	+	12.0388i	1.02407	+	0.421700i
$816$	11.1415	+	5.58489i	0.390029	+	0.195510i
$817$	10.8205	−	19.8162i	0.378560	−	0.693281i
$818$	33.3778	+	23.6260i	1.16703	+	0.826064i
$819$	−13.9789	+	2.00986i	−0.488463	+	0.0702303i
$820$	−29.5314	−	12.7918i	−1.03128	−	0.446708i
$821$	4.51810	−	2.06335i	0.157683	−	0.0720113i	−0.335010	−	0.942214i	$-0.608740\pi$
$821$	4.51810	−	2.06335i	0.157683	−	0.0720113i	0.492693	+	0.870203i	$0.336013\pi$
$822$	−7.73337	+	3.12143i	−0.269732	+	0.108872i
$823$	32.8679	−	24.6046i	1.14570	−	0.857663i	0.154239	−	0.988034i	$-0.450708\pi$
$823$	32.8679	−	24.6046i	1.14570	−	0.857663i	0.991465	+	0.130370i	$0.0416166\pi$
$824$	−31.4095	−	11.4119i	−1.09420	−	0.397554i
$825$	−16.6727	+	2.46771i	−0.580470	+	0.0859147i
$826$	−3.68973	−	11.4307i	−0.128382	−	0.397724i
$827$	−37.1958	+	37.1958i	−1.29342	+	1.29342i	−0.360769	+	0.932655i	$0.617486\pi$
$827$	−37.1958	+	37.1958i	−1.29342	+	1.29342i	−0.932655	+	0.360769i	$0.882514\pi$
$828$	17.9913	+	18.7143i	0.625240	+	0.650367i
$829$	−39.6582			−1.37739			−0.688694	−	0.725052i	$-0.741816\pi$
$829$	−39.6582			−1.37739			−0.688694	+	0.725052i	$0.741816\pi$
$830$	34.0949	+	15.8598i	1.18345	+	0.550501i
$831$	2.97987	−	3.43895i	0.103371	−	0.119296i
$832$	−16.6297	−	21.4448i	−0.576532	−	0.743465i
$833$	15.9702	+	21.3336i	0.553334	+	0.739167i
$834$	−1.17710	+	2.77047i	−0.0407598	+	0.0959334i
$835$	23.5248	−	11.8367i	0.814110	−	0.409625i
$836$	−66.0529	+	23.2812i	−2.28449	+	0.805196i
$837$	−10.6231	+	14.1909i	−0.367190	+	0.490508i
$838$	35.3567	+	25.0267i	1.22138	+	0.864532i
$839$	−52.0635	+	15.2872i	−1.79743	+	0.527773i	−0.997392	−	0.0721751i	$-0.977006\pi$
$839$	−52.0635	+	15.2872i	−1.79743	+	0.527773i	−0.800039	+	0.599948i	$0.795188\pi$
$840$	−4.50421	+	2.73726i	−0.155410	+	0.0944445i
$841$	−1.18944	+	2.60451i	−0.0410152	+	0.0898107i
$842$	−2.49663	+	55.7332i	−0.0860395	+	1.92069i
$843$	0.971506	−	13.5834i	0.0334604	−	0.467838i
$844$	−6.28466	+	0.335085i	−0.216327	+	0.0115341i
$845$	−3.28731	−	0.586068i	−0.113087	−	0.0201614i
$846$	10.3931	−	5.08511i	0.357322	−	0.174830i
$847$	9.06217	+	41.6581i	0.311380	+	1.43139i
$848$	22.7054	+	18.3183i	0.779706	+	0.629053i
$849$	0.00924116	+	0.00271345i	0.000317156	+	9.31253e-5i
$850$	31.7899	−	25.3608i	1.09039	−	0.869867i
$851$	43.2473	+	32.4802i	1.48250	+	1.11341i
$852$	1.44990	−	0.630629i	0.0496726	−	0.0216050i
$853$	−2.19909	+	1.20079i	−0.0752953	+	0.0411143i	−0.516456	−	0.856314i	$-0.672749\pi$
$853$	−2.19909	+	1.20079i	−0.0752953	+	0.0411143i	0.441160	+	0.897428i	$0.354567\pi$
$854$	15.1407	+	1.76679i	0.518104	+	0.0604582i
$855$	−32.9846	+	8.49161i	−1.12805	+	0.290407i
$856$	−2.67139	−	33.3626i	−0.0913063	−	1.14031i
$857$	−7.73510	+	35.5577i	−0.264226	+	1.21463i	0.633384	+	0.773838i	$0.281665\pi$
$857$	−7.73510	+	35.5577i	−0.264226	+	1.21463i	−0.897610	+	0.440790i	$0.854698\pi$
$858$	15.7042	−	3.85694i	0.536131	−	0.131674i
$859$	0.753678	+	0.869791i	0.0257152	+	0.0296769i	0.768461	−	0.639896i	$-0.221023\pi$
$859$	0.753678	+	0.869791i	0.0257152	+	0.0296769i	−0.742746	+	0.669573i	$0.766477\pi$
$860$	3.46864	−	17.6025i	0.118280	−	0.600240i
$861$	2.49133	−	5.45524i	0.0849042	−	0.185914i
$862$	3.15717	+	32.1017i	0.107534	+	1.09339i
$863$	−5.78686	−	3.15986i	−0.196987	−	0.107563i	0.377728	−	0.925916i	$-0.376705\pi$
$863$	−5.78686	−	3.15986i	−0.196987	−	0.107563i	−0.574715	+	0.818353i	$0.694887\pi$
$864$	−14.6205	−	9.59621i	−0.497398	−	0.326470i
$865$	21.1837	−	3.86727i	0.720266	−	0.131491i
$866$	15.7139	+	4.16284i	0.533980	+	0.141459i
$867$	3.04347	−	8.15986i	0.103362	−	0.277123i
$868$	14.6648	+	9.80472i	0.497757	+	0.332794i
$869$	6.01857	−	41.8601i	0.204166	−	1.42001i
$870$	−5.78179	+	6.57898i	−0.196021	+	0.223048i
$871$	17.3994	+	15.0767i	0.589557	+	0.510854i
$872$	−6.36488	+	5.61064i	−0.215542	+	0.190000i
$873$	−27.3649	+	27.3649i	−0.926160	+	0.926160i
$874$	−33.0327	+	19.1274i	−1.11735	+	0.646995i
$875$	1.94464	+	17.0881i	0.0657408	+	0.577684i
$876$	−2.49656	−	1.94051i	−0.0843508	−	0.0655639i
$877$	−29.8576	+	2.13546i	−1.00822	+	0.0721094i	−0.565668	−	0.824633i	$-0.691382\pi$
$877$	−29.8576	+	2.13546i	−1.00822	+	0.0721094i	−0.442553	+	0.896742i	$0.645927\pi$
$878$	−23.4945	+	24.7806i	−0.792902	+	0.836304i
$879$	0.0366092	−	0.254622i	0.00123480	−	0.00858820i
$880$	−44.5015	+	33.4181i	−1.50015	+	1.12652i
$881$	−38.2284	+	17.4583i	−1.28795	+	0.588185i	−0.937366	−	0.348347i	$-0.886743\pi$
$881$	−38.2284	+	17.4583i	−1.28795	+	0.588185i	−0.350580	+	0.936533i	$0.614016\pi$
$882$	−8.91141	−	15.3345i	−0.300063	−	0.516339i
$883$	−44.3695	−	33.2146i	−1.49315	−	1.11776i	−0.962879	−	0.269935i	$-0.912998\pi$
$883$	−44.3695	−	33.2146i	−1.49315	−	1.11776i	−0.530275	−	0.847826i	$-0.677911\pi$
$884$	−28.0851	+	27.0846i	−0.944604	+	0.910955i
$885$	2.12541	+	6.34196i	0.0714448	+	0.213183i
$886$	5.12885	−	6.24772i	0.172307	−	0.209896i
$887$	−2.71220	−	7.27170i	−0.0910668	−	0.244160i	0.883429	−	0.468565i	$-0.155229\pi$
$887$	−2.71220	−	7.27170i	−0.0910668	−	0.244160i	−0.974496	+	0.224405i	$0.927956\pi$
$888$	−15.7799	−	7.04494i	−0.529540	−	0.236413i
$889$	1.43889	+	1.66056i	0.0482587	+	0.0556935i
$890$	18.6864	+	10.3739i	0.626371	+	0.347734i
$891$	−33.7334	+	21.6792i	−1.13011	+	0.726279i
$892$	−35.2568	+	9.66152i	−1.18048	+	0.323491i
$893$	3.61637	+	16.6242i	0.121017	+	0.556307i
$894$	−12.3061	−	1.43601i	−0.411577	−	0.0480275i
$895$	50.9101	−	30.3491i	1.70174	−	1.01446i
$896$	−8.76146	+	15.0373i	−0.292700	+	0.502362i
$897$	8.02270	−	3.64870i	0.267870	−	0.121826i
$898$	0.145934	−	0.768897i	0.00486989	−	0.0256584i
$899$	28.1266	+	8.25870i	0.938073	+	0.275443i
$900$	−22.9710	+	14.3125i	−0.765699	+	0.477082i
$901$	22.6772	−	35.2865i	0.755488	−	1.17556i
$902$	20.5412	−	59.8985i	0.683947	−	1.99440i
$903$	3.26687	+	0.710663i	0.108714	+	0.0236494i
$904$	−9.75724	−	12.8058i	−0.324521	−	0.425913i
$905$	−33.4904	−	1.12667i	−1.11326	−	0.0374517i
$906$	1.57243	+	1.71991i	0.0522403	+	0.0571402i
$907$	−2.42503	−	6.50175i	−0.0805217	−	0.215887i	0.890450	−	0.455081i	$-0.150390\pi$
$907$	−2.42503	−	6.50175i	−0.0805217	−	0.215887i	−0.970972	+	0.239194i	$0.923117\pi$
$908$	10.7636	−	8.99029i	0.357204	−	0.298353i
$909$	−13.8376	+	4.06308i	−0.458964	+	0.134764i
$910$	−3.39466	−	16.1480i	−0.112532	−	0.535301i
$911$	41.5917	−	5.97999i	1.37800	−	0.198126i	0.586821	−	0.809716i	$-0.300379\pi$
$911$	41.5917	−	5.97999i	1.37800	−	0.198126i	0.791175	+	0.611590i	$0.209470\pi$
$912$	8.93092	−	8.30556i	0.295732	−	0.275025i
$913$	−25.8561	+	69.3228i	−0.855711	+	2.29425i
$914$	27.2308	+	11.5697i	0.900716	+	0.382692i
$915$	−8.44161	−	0.889885i	−0.279071	−	0.0294187i
$916$	−27.8386	+	20.0625i	−0.919812	+	0.662884i
$917$	−0.0570891	−	0.798210i	−0.00188525	−	0.0263592i
$918$	−11.4585	+	22.3819i	−0.378187	+	0.738712i
$919$	15.7443			0.519356			0.259678	−	0.965695i	$-0.416383\pi$
$919$	15.7443			0.519356			0.259678	+	0.965695i	$0.416383\pi$
$920$	−20.4676	+	22.3848i	−0.674797	+	0.738004i
$921$	7.65999			0.252405
$922$	−10.1529	+	19.8316i	−0.334367	+	0.653120i
$923$	0.353124	+	4.93732i	0.0116232	+	0.162514i
$924$	−6.06335	−	8.41346i	−0.199470	−	0.276782i
$925$	−42.4623	+	37.1028i	−1.39615	+	1.21993i
$926$	−1.21233	−	0.515091i	−0.0398398	−	0.0169269i
$927$	11.1751	−	29.9616i	0.367038	−	0.984067i
$928$	−6.41930	+	28.1987i	−0.210724	+	0.925669i
$929$	52.6034	−	7.56322i	1.72586	−	0.248141i	0.793217	−	0.608939i	$-0.208405\pi$
$929$	52.6034	−	7.56322i	1.72586	−	0.248141i	0.932644	+	0.360798i	$0.117496\pi$
$930$	−8.22649	−	5.36853i	−0.269757	−	0.176041i
$931$	25.0221	−	7.34716i	0.820067	−	0.240793i
$932$	0.0869109	+	0.104054i	0.00284686	+	0.00340841i
$933$	3.51344	+	9.41990i	0.115025	+	0.308394i
$934$	11.8458	+	12.9568i	0.387605	+	0.423960i
$935$	54.6451	+	58.4498i	1.78709	+	1.91151i
$936$	20.6549	−	15.7378i	0.675126	−	0.514407i
$937$	39.3397	+	8.55782i	1.28517	+	0.279572i	0.802723	−	0.596353i	$-0.203384\pi$
$937$	39.3397	+	8.55782i	1.28517	+	0.279572i	0.482448	+	0.875924i	$0.339748\pi$
$938$	4.78956	−	13.9665i	0.156385	−	0.456021i
$939$	−5.52640	+	8.59925i	−0.180347	+	0.280626i
$940$	6.71068	+	11.7358i	0.218878	+	0.382778i
$941$	0.177437	+	0.0521002i	0.00578429	+	0.00169842i	0.284623	−	0.958639i	$-0.408131\pi$
$941$	0.177437	+	0.0521002i	0.00578429	+	0.00169842i	−0.278839	+	0.960338i	$0.589950\pi$
$942$	−1.36600	+	7.19719i	−0.0445068	+	0.234497i
$943$	4.96499	−	34.1532i	0.161682	−	1.11218i
$944$	16.1557	+	15.0586i	0.525824	+	0.490114i
$945$	−5.44511	−	9.13409i	−0.177130	−	0.297132i
$946$	35.0628	+	4.09152i	1.13999	+	0.133027i
$947$	5.15041	+	23.6760i	0.167366	+	0.769368i	0.981922	+	0.189284i	$0.0606166\pi$
$947$	5.15041	+	23.6760i	0.167366	+	0.769368i	−0.814557	+	0.580084i	$0.803020\pi$
$948$	1.94636	+	7.10264i	0.0632148	+	0.230683i
$949$	8.32781	−	5.35196i	0.270332	−	0.173732i
$950$	−12.3814	−	37.8208i	−0.401707	−	1.22707i
$951$	0.720357	+	0.831336i	0.0233592	+	0.0269579i
$952$	22.8488	+	10.2009i	0.740534	+	0.330611i
$953$	−14.9771	−	40.1551i	−0.485156	−	1.30075i	−0.917030	−	0.398819i	$-0.869420\pi$
$953$	−14.9771	−	40.1551i	−0.485156	−	1.30075i	0.431874	−	0.901934i	$-0.357852\pi$
$954$	−17.7127	+	21.5768i	−0.573470	+	0.698574i
$955$	21.3907	+	10.6521i	0.692187	+	0.344693i
$956$	−19.8849	−	20.6194i	−0.643124	−	0.666880i
$957$	−13.7960	−	10.3275i	−0.445960	−	0.333842i
$958$	−25.8519	−	44.4853i	−0.835238	−	1.43725i
$959$	−15.2308	+	6.95565i	−0.491827	+	0.224610i
$960$	4.78531	−	8.42744i	0.154445	−	0.271994i
$961$	−0.267191	+	1.85835i	−0.00861907	+	0.0599469i
$962$	37.2233	−	39.2609i	1.20013	−	1.26582i
$963$	31.9449	−	2.28475i	1.02941	−	0.0736249i
$964$	13.9975	−	18.0084i	0.450830	−	0.580013i
$965$	18.0874	−	0.683507i	0.582256	−	0.0220029i
$966$	−4.09565	−	3.89527i	−0.131775	−	0.125328i
$967$	1.71895	−	1.71895i	0.0552778	−	0.0552778i	−0.678928	−	0.734205i	$-0.737555\pi$
$967$	1.71895	−	1.71895i	0.0552778	−	0.0552778i	0.734205	+	0.678928i	$0.237555\pi$
$968$	−51.8352	−	58.8034i	−1.66605	−	1.89001i
$969$	−13.2522	−	11.4831i	−0.425723	−	0.368891i
$970$	−33.9647	−	29.8491i	−1.09054	−	0.958396i
$971$	3.08912	−	21.4853i	0.0991345	−	0.689495i	−0.878277	−	0.478152i	$-0.841307\pi$
$971$	3.08912	−	21.4853i	0.0991345	−	0.689495i	0.977412	−	0.211344i	$-0.0677840\pi$
$972$	14.1909	−	21.2252i	0.455173	−	0.680798i
$973$	−2.11205	+	5.66263i	−0.0677093	+	0.181536i
$974$	−33.8042	−	8.95521i	−1.08316	−	0.286943i
$975$	1.99036	+	8.97049i	0.0637426	+	0.287285i
$976$	−25.9007	+	10.7113i	−0.829060	+	0.342859i
$977$	−51.6949	−	28.2276i	−1.65387	−	0.903080i	−0.987530	−	0.157430i	$-0.949679\pi$
$977$	−51.6949	−	28.2276i	−1.65387	−	0.903080i	−0.666337	−	0.745650i	$-0.732139\pi$
$978$	−1.06032	−	10.7812i	−0.0339052	−	0.344744i
$979$	−17.4696	+	38.2530i	−0.558330	+	1.22257i
$980$	17.2096	−	11.5437i	0.549740	−	0.368749i
$981$	−5.31681	−	6.13592i	−0.169753	−	0.195905i
$982$	52.7943	−	12.9663i	1.68473	−	0.413770i
$983$	3.22018	−	14.8029i	0.102708	−	0.472141i	−0.896848	−	0.442339i	$-0.854149\pi$
$983$	3.22018	−	14.8029i	0.102708	−	0.472141i	0.999556	−	0.0298016i	$-0.00948754\pi$
$984$	0.880137	+	10.9919i	0.0280577	+	0.350408i
$985$	35.6995	+	21.0817i	1.13748	+	0.671718i
$986$	41.3006	+	4.81942i	1.31528	+	0.153482i
$987$	−2.21107	+	1.20734i	−0.0703792	+	0.0384299i
$988$	15.2290	+	35.0134i	0.484500	+	1.11393i
$989$	19.1927	−	1.34253i	0.610292	−	0.0426901i
$990$	−31.6143	−	42.8534i	−1.00477	−	1.36197i
$991$	−31.0418	−	9.11469i	−0.986075	−	0.289538i	−0.251345	−	0.967898i	$-0.580873\pi$
$991$	−31.0418	−	9.11469i	−0.986075	−	0.289538i	−0.734730	+	0.678360i	$0.762691\pi$
$992$	−32.3293	−	2.62543i	−1.02646	−	0.0833574i
$993$	−2.37241	−	10.9058i	−0.0752861	−	0.346085i
$994$	2.85147	−	1.39516i	0.0904431	−	0.0442517i
$995$	−1.35278	+	7.58784i	−0.0428859	+	0.240551i
$996$	−0.685987	−	12.8660i	−0.0217363	−	0.407675i
$997$	−1.73999	+	24.3283i	−0.0551062	+	0.770485i	0.892501	+	0.451046i	$0.148949\pi$
$997$	−1.73999	+	24.3283i	−0.0551062	+	0.770485i	−0.947607	+	0.319439i	$0.896506\pi$
$998$	1.99839	−	44.6109i	0.0632580	−	1.41213i
$999$	14.4837	−	31.7148i	0.458243	−	1.00341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bo.a.373.23	yes	2800
5.2	odd	4	inner	920.2.bo.a.557.94	yes	2800
8.5	even	2	inner	920.2.bo.a.373.69	yes	2800
23.14	odd	22	inner	920.2.bo.a.773.3	yes	2800
40.37	odd	4	inner	920.2.bo.a.557.3	yes	2800
115.37	even	44	inner	920.2.bo.a.37.69	yes	2800
184.37	odd	22	inner	920.2.bo.a.773.94	yes	2800
920.37	even	44	inner	920.2.bo.a.37.23	✓	2800

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bo.a.37.23	✓	2800	920.37	even	44	inner
920.2.bo.a.37.69	yes	2800	115.37	even	44	inner
920.2.bo.a.373.23	yes	2800	1.1	even	1	trivial
920.2.bo.a.373.69	yes	2800	8.5	even	2	inner
920.2.bo.a.557.3	yes	2800	40.37	odd	4	inner
920.2.bo.a.557.94	yes	2800	5.2	odd	4	inner
920.2.bo.a.773.3	yes	2800	23.14	odd	22	inner
920.2.bo.a.773.94	yes	2800	184.37	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bo (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25883 - 0.644466i) q^{2} +(-0.0386486 - 0.540379i) q^{3} +(1.16933 + 1.62255i) q^{4} +(-1.40667 - 1.73819i) q^{5} +(-0.299603 + 0.705155i) q^{6} +(-0.537572 + 1.44129i) q^{7} +(-0.426313 - 2.79611i) q^{8} +(2.67895 - 0.385175i) q^{9} +O(q^{10})\)	\(q+(-1.25883 - 0.644466i) q^{2} +(-0.0386486 - 0.540379i) q^{3} +(1.16933 + 1.62255i) q^{4} +(-1.40667 - 1.73819i) q^{5} +(-0.299603 + 0.705155i) q^{6} +(-0.537572 + 1.44129i) q^{7} +(-0.426313 - 2.79611i) q^{8} +(2.67895 - 0.385175i) q^{9} +(0.650559 + 3.09464i) q^{10} +(-5.97005 + 1.75297i) q^{11} +(0.831599 - 0.694590i) q^{12} +(1.18544 + 3.17828i) q^{13} +(1.60557 - 1.46789i) q^{14} +(-0.884913 + 0.827311i) q^{15} +(-1.26534 + 3.79459i) q^{16} +(5.61969 + 1.22249i) q^{17} +(-3.62058 - 1.24162i) q^{18} +(3.04272 - 4.73456i) q^{19} +(1.17544 - 4.31490i) q^{20} +(0.799616 + 0.234788i) q^{21} +(8.64504 + 1.64080i) q^{22} +(4.79583 + 0.00749698i) q^{23} +(-1.49448 + 0.338436i) q^{24} +(-1.04258 + 4.89009i) q^{25} +(0.556022 - 4.76489i) q^{26} +(-0.657155 - 3.02090i) q^{27} +(-2.96716 + 0.813098i) q^{28} +(-4.30083 + 2.76398i) q^{29} +(1.64713 - 0.471152i) q^{30} +(-3.75490 - 4.33338i) q^{31} +(4.03834 - 3.96129i) q^{32} +(1.17800 + 3.15834i) q^{33} +(-6.28640 - 5.16060i) q^{34} +(3.26140 - 1.09301i) q^{35} +(3.75754 + 3.89634i) q^{36} +(9.02827 + 6.75848i) q^{37} +(-6.88154 + 3.99910i) q^{38} +(1.67166 - 0.763420i) q^{39} +(-4.26049 + 4.67421i) q^{40} +(1.02414 - 7.12304i) q^{41} +(-0.855271 - 0.810885i) q^{42} +(4.00151 - 0.286194i) q^{43} +(-9.82523 - 7.63692i) q^{44} +(-4.43789 - 4.11470i) q^{45} +(-6.03232 - 3.10018i) q^{46} +(-2.13753 + 2.13753i) q^{47} +(2.09942 + 0.537108i) q^{48} +(3.50193 + 3.03444i) q^{49} +(4.46393 - 5.48391i) q^{50} +(0.443413 - 3.08401i) q^{51} +(-3.77075 + 5.63988i) q^{52} +(2.54878 - 6.83353i) q^{53} +(-1.11961 + 4.22632i) q^{54} +(11.4449 + 7.91122i) q^{55} +(4.25917 + 0.888673i) q^{56} +(-2.67605 - 1.46124i) q^{57} +(7.19533 - 0.707652i) q^{58} +(2.29366 - 5.02241i) q^{59} +(-2.37711 - 0.468418i) q^{60} +(4.58863 + 5.29556i) q^{61} +(1.93408 + 7.87491i) q^{62} +(-0.884980 + 4.06819i) q^{63} +(-7.63651 + 2.38404i) q^{64} +(3.85692 - 6.53128i) q^{65} +(0.552534 - 4.73501i) q^{66} +(5.95686 - 3.25269i) q^{67} +(4.58771 + 10.5477i) q^{68} +(-0.181301 - 2.59185i) q^{69} +(-4.80997 - 0.725947i) q^{70} +(1.40012 + 0.411113i) q^{71} +(-2.21906 - 7.32644i) q^{72} +(-0.620328 - 2.85160i) q^{73} +(-7.00949 - 14.3262i) q^{74} +(2.68280 + 0.374392i) q^{75} +(11.2400 - 0.599293i) q^{76} +(0.682807 - 9.54689i) q^{77} +(-2.59634 - 0.116306i) q^{78} +(-2.82351 + 6.18262i) q^{79} +(8.37562 - 3.13832i) q^{80} +(6.18357 - 1.81566i) q^{81} +(-5.87978 + 8.30671i) q^{82} +(7.12610 - 9.51935i) q^{83} +(0.554058 + 1.57196i) q^{84} +(-5.78011 - 11.4877i) q^{85} +(-5.22168 - 2.21856i) q^{86} +(1.65982 + 2.21725i) q^{87} +(7.44660 + 15.9456i) q^{88} +(4.42601 - 5.10789i) q^{89} +(2.93479 + 8.03979i) q^{90} -5.21806 q^{91} +(5.59573 + 7.79024i) q^{92} +(-2.19655 + 2.19655i) q^{93} +(4.06836 - 1.31323i) q^{94} +(-12.5096 + 1.37114i) q^{95} +(-2.29667 - 2.02913i) q^{96} +(-11.4468 + 8.56897i) q^{97} +(-2.45276 - 6.07673i) q^{98} +(-15.3183 + 6.99562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8}+O(q^{10}) \) 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8	\( 2800 q - 18 q^{2} - 28 q^{6} - 44 q^{7} - 18 q^{8} - 22 q^{10} - 6 q^{12} - 44 q^{15} - 44 q^{16} - 44 q^{17} - 38 q^{18} - 22 q^{20} - 40 q^{23} - 36 q^{25} - 36 q^{26} - 22 q^{28} - 22 q^{30} - 104 q^{31} - 38 q^{32} - 44 q^{33} - 36 q^{36} - 22 q^{38} - 22 q^{40} - 72 q^{41} + 198 q^{42} - 28 q^{46} - 80 q^{47} - 10 q^{48} - 2 q^{50} - 146 q^{52} + 4 q^{55} - 44 q^{56} - 44 q^{57} - 42 q^{58} - 22 q^{60} + 46 q^{62} - 44 q^{63} - 44 q^{65} - 44 q^{66} - 64 q^{70} - 72 q^{71} - 104 q^{72} - 36 q^{73} - 44 q^{76} - 114 q^{78} - 220 q^{80} + 176 q^{81} - 10 q^{82} - 44 q^{86} - 12 q^{87} - 22 q^{88} - 440 q^{90} - 2 q^{92} - 76 q^{95} - 124 q^{96} - 44 q^{97} + 30 q^{98}+O(q^{100}) \) 2800 * q - 18 * q^2 - 28 * q^6 - 44 * q^7 - 18 * q^8 - 22 * q^10 - 6 * q^12 - 44 * q^15 - 44 * q^16 - 44 * q^17 - 38 * q^18 - 22 * q^20 - 40 * q^23 - 36 * q^25 - 36 * q^26 - 22 * q^28 - 22 * q^30 - 104 * q^31 - 38 * q^32 - 44 * q^33 - 36 * q^36 - 22 * q^38 - 22 * q^40 - 72 * q^41 + 198 * q^42 - 28 * q^46 - 80 * q^47 - 10 * q^48 - 2 * q^50 - 146 * q^52 + 4 * q^55 - 44 * q^56 - 44 * q^57 - 42 * q^58 - 22 * q^60 + 46 * q^62 - 44 * q^63 - 44 * q^65 - 44 * q^66 - 64 * q^70 - 72 * q^71 - 104 * q^72 - 36 * q^73 - 44 * q^76 - 114 * q^78 - 220 * q^80 + 176 * q^81 - 10 * q^82 - 44 * q^86 - 12 * q^87 - 22 * q^88 - 440 * q^90 - 2 * q^92 - 76 * q^95 - 124 * q^96 - 44 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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